WAEC SSCE - Physics - 2014

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When a ball falls through a viscous liquid, it is acted upon by three main forces: upthrust, weight, and viscous force. Upthrust is the upward force that acts on an object when it is partially or completely submerged in a liquid. The ball's weight is the force with which the ball is pulled down by gravity. The viscous force is a force that opposes the motion of an object through a fluid, such as air or a liquid. Therefore, the correct answer is "upthrust, the ball's weight and viscous force".

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The region around a magnet in which magnetic force can be expressed is known as a magnetic field. Magnetic field lines are used to represent the magnetic field, and the direction of the lines shows the direction of the magnetic force at any point in the field. The strength of the magnetic field is measured in terms of its flux density, which is the amount of magnetic flux passing through a unit area perpendicular to the direction of the magnetic field. The other options listed are not correct definitions of the region around a magnet in which magnetic force can be expressed.

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The resistivity (\(\rho\)) of a material is a measure of how resistant the material is to the flow of an electric current through it. It is defined as the resistance (\(R\)) of a conductor of unit length (\(l\)) and unit cross-sectional area (\(A\)). The formula for resistivity is: \(\rho = RA/l\). We are given the length (\(l\)) of the wire as 100 cm, its resistance (\(R\)) as 10\(\Omega\), and its cross-sectional area (\(A\)) as 0.005cm². To find the resistivity (\(\rho\)), we rearrange the formula as \(\rho = RA/l\). Substituting the values we have, we get: \(\rho = (10\Omega)(0.005cm^2)/100cm = 0.0005\Omega cm\). Therefore, the resistivity of the wire is 0.0005\(\Omega\)cm. The correct option is (a).

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An aluminum foil is not thick enough to stop alpha and beta particles as they have high energy and mass, and can penetrate thin materials. However, gamma particles have high energy but no mass, and can only be stopped by thick and dense materials such as lead or concrete. Therefore, the correct answer is (d) gamma particles only, as they will not be stopped by the aluminum foil.

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A device that converts mechanical energy into electrical energy is a dynamo. A dynamo works by using a rotating coil of wire that is placed between the poles of a magnet. When the coil rotates, it cuts through the magnetic field lines, which induces an electrical current in the coil. The amount of electrical energy produced by the dynamo depends on factors such as the strength of the magnetic field, the speed at which the coil rotates, and the number of turns in the coil. Dynamos are commonly used in bicycles to generate electrical power to power lights, and in power plants to generate electricity on a large scale.

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The SI unit of power is W, which stands for Watt. Power is a measure of how much energy is used or transferred per unit time. One watt is equivalent to one joule of energy per second. Therefore, power is usually measured in watts, which provides an indication of how much energy is being used or transferred per unit time.

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The energy stored in a simple cell is chemical energy. A simple cell is an electrochemical device that converts chemical energy into electrical energy. The chemical reactions taking place within the cell create a potential difference between the electrodes, and when a circuit is completed between the electrodes, electrons flow through the circuit, producing an electrical current. The chemical energy is stored in the reactants of the cell, which are typically stored in separate compartments within the cell until the cell is activated by connecting the electrodes. As the chemical reactions proceed, the reactants are converted into products, and the energy difference between the reactants and products is released as electrical energy.

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The density of a substance is defined as its mass per unit volume. In this question, we are given the mass and density of alcohol and the mass and density of water. We can find the total volume of the mixture by adding the volumes of alcohol and water. The volume of alcohol is calculated as follows: Volume of alcohol = mass of alcohol/density of alcohol Volume of alcohol = 21g/0.7gcm^-3 Volume of alcohol = 30cm³ The volume of water is equal to its mass, which is 10g. The total volume of the mixture is: Total volume = volume of alcohol + volume of water Total volume = 30cm³ + 10cm³ Total volume = 40cm³ The mass of the mixture is the sum of the mass of alcohol and water: Mass of mixture = mass of alcohol + mass of water Mass of mixture = 21g + 10g Mass of mixture = 31g The density of the mixture is therefore: Density of mixture = mass of mixture/total volume Density of mixture = 31g/40cm³ Density of mixture = 0.775gcm^-3 Therefore, the density of the mixture is 0.775gcm^-3. Option A is the correct answer.

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An alpha particle is a helium nucleus that contains two protons and two neutrons. When an alpha particle is emitted from a nucleus, the nucleus loses two protons and two neutrons. Therefore, the atomic number of the new element formed will be reduced by two and the nucleon number will be reduced by four. So, the resultant numbers of the new element formed are P - 4 and Q - 2. Therefore, the correct option is (b) P - 4 and Q - 2.

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A transformer is an electrical device used to transfer electrical energy from one circuit to another by means of electromagnetic induction. It works on the principle that a changing magnetic field in a coil of wire induces a voltage in another coil of wire placed close to it. The ratio of the number of turns in the primary coil to the number of turns in the secondary coil is called the turns ratio. In this case, the turns ratio is 400:40, which reduces to 10:1. This means that the voltage in the secondary coil is one-tenth of the voltage in the primary coil. So, if the input voltage is 150 volts, the output voltage will be 15 volts. Therefore, the correct option is: - 15V

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The correct answer is "nuclear binding energy". The energy required to separate the nucleus in an atom completely is called the nuclear binding energy. It is the energy needed to overcome the strong force, which is the force that holds the nucleus together. This energy is released when the nucleus is formed, and it is also released in nuclear reactions such as fusion and fission. The other options listed, mass defect of the atom, electron binding energy, and excitation energy, are all different concepts that are not directly related to the energy required to completely separate a nucleus.

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When an elastic material is stretched by a force, it stores potential energy. The potential energy is stored in the material due to its ability to return to its original shape when the force is removed. The energy is stored as a result of the deformation of the material from its original shape. The more the material is stretched, the more potential energy it stores. This stored energy can be released when the material returns to its original shape, such as when the force is removed.

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A screw jack is a simple machine used for lifting heavy loads. The velocity ratio of a machine is defined as the ratio of the distance moved by the effort to the distance moved by the load. In the case of a screw jack, the effort is applied through a tommy bar, which is used to turn the screw. The distance moved by the effort is the circumference of the circle described by the end of the tommy bar, which is 2πr. The load is lifted by the screw, which has a thread pitch of P, which is the distance between successive threads. The distance moved by the load is equal to the pitch of the screw. Therefore, the velocity ratio of a screw jack is given by the expression: velocity ratio = distance moved by effort / distance moved by load velocity ratio = 2πr / P Thus, the correct option is: \(\frac{2 \pi r}{P}\)

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A lens and a mirror are both optical devices that are used to manipulate the path of light. The functional difference between a lens and a mirror is that a lens refracts a beam of light while a mirror reflects it. A lens is a piece of glass or other transparent material that bends light as it passes through it, while a mirror is a surface that reflects light. When light passes through a lens, it is bent in such a way that the image formed is either magnified or diminished, depending on the shape of the lens. In contrast, when light hits a mirror, it is reflected back in the opposite direction, producing a virtual image of the object being reflected.

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The formula for the speed of a wave is given as: speed = wavelength x frequency Since we are given the speed of the electromagnetic wave as 3.0 x 10^8 ms^-1, we can find the wavelength of the wave using the formula: wavelength = speed / frequency However, the frequency of the wave is not given in the question, so we cannot directly calculate the wavelength. Therefore, we need to use the information in the diagram to find the frequency. The diagram shows that the wave has 6 complete cycles in a distance of 0.96 meters. The distance of 6 complete cycles is equal to the wavelength of the wave. Therefore, we can find the wavelength by dividing the distance of 6 complete cycles by 6: wavelength = 0.96 m / 6 = 0.16 m Therefore, the wavelength of the electromagnetic wave is 0.16 meters. Answer: 0.16m

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The thermometer that can be used to measure a range of temperature from -50°C to 50°C is the alcohol-in-glass thermometer. Therefore, the correct answer is (iii) only. Clinical thermometers are used to measure body temperature and usually have a range of 35°C to 42°C. Mercury thermometers, on the other hand, have a range of -38°C to 356°C but are not suitable for measuring temperatures below -38°C. Alcohol-in-glass thermometers, with their low freezing point, are suitable for measuring a wider range of temperatures, including those below -38°C.

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An electric motor converts electrical energy to mechanical energy. The motor uses an electromagnetic field to create rotational motion in its output shaft. When an electric current passes through the wire coils of the motor, a magnetic field is generated. The magnetic field interacts with the field generated by a stationary component of the motor, causing the rotor to rotate. This rotation creates mechanical energy in the form of rotational motion, which can be used to power various machines or devices. Therefore, the conversion of electrical energy to mechanical energy is the main function of an electric motor.

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Power is the rate at which work is done or the rate at which energy is transferred. In this question, the power developed by the car's engine can be calculated using the formula: Power = force x velocity The force in this case is the frictional resistance, which is 100N, and the velocity is 30ms\(^{-1}\). Therefore, Power = 100N x 30ms\(^{-1}\) = 3000W = 3kW To convert kW to hp, we use the conversion factor 1 hp = 0.75 kW. 3 kW = 3/0.75 hp = 4 hp Therefore, the power developed by the engine is 4 hp, which corresponds to the.

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When the temperature of the resistor R is increased, its resistance increases. Since the resistor R and the lamp L are connected in series, the total resistance of the circuit also increases. This causes a decrease in the current passing through the circuit since current is inversely proportional to resistance (Ohm's law). As a result, the brightness of the lamp L decreases slightly. Therefore, the correct answer is "decrease slightly."

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In an AC circuit, when the supply voltage frequency is equal to the resonant frequency, the current is in phase with the supply voltage. This means that the current and voltage signals reach their maximum and minimum values at the same time and change direction at the same time. There is no phase shift between them. This is because at resonant frequency, the inductive reactance of the inductor and the capacitive reactance of the capacitor are equal in magnitude but opposite in sign. This results in cancelling out each other's effect and hence the circuit impedance becomes purely resistive. Therefore, the current flowing in the circuit is limited by the resistance of the circuit alone and is in phase with the voltage across the circuit.

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The temperature at which the water vapor in the air saturates the air and begins to condense is known as the "dew point". When air is cooled down to its dew point temperature, the air is no longer able to hold all the water vapor it contains and some of it condenses into water droplets, forming dew. Therefore, the dew point is the temperature at which the relative humidity of the air reaches 100%, and further cooling will result in the formation of dew, fog, or clouds.

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Surface tension is a property of liquids that describes the ability of the surface of a liquid to resist an external force due to the cohesive nature of its molecules. It has many applications in various fields such as engineering, physics, and chemistry. However, the production of palm oil does not require the application of surface tension. The process of producing palm oil involves the extraction of oil from palm fruit using mechanical pressing or solvent extraction methods, which do not rely on the surface tension of liquids. Therefore, the correct answer is "production of palm oil."

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When a sound wave is produced, it travels through the air with a certain speed. When it reaches a surface such as a wall, a portion of the sound energy is reflected back to the source as an echo. To calculate the distance of the observer from the cliff, we need to first determine the distance travelled by the sound wave. Since the sound wave travels to the cliff and then back to the observer, the total distance travelled is twice the distance from the observer to the cliff. We can use the formula: distance = speed x time where speed is the speed of sound in air and time is the time between the sound wave being produced and the echo being heard. In this case, the time is given as 1.26 seconds and the speed of sound in air is given as 330 m/s. Therefore, the distance travelled by the sound wave is: distance = speed x time distance = 330 m/s x 1.26 s distance = 415.8 m Since the sound wave travels twice the distance from the observer to the cliff, we need to divide the distance travelled by 2 to find the distance from the observer to the cliff: distance from observer to cliff = 415.8 m / 2 distance from observer to cliff = 207.9 m Therefore, the distance of the observer from the cliff is 207.9 meters. The correct option is: 207.9m

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At resonance in a series RLC circuit, the reactance of the inductor and capacitor cancel each other out, leaving only the resistance. This means the impedance of the circuit is equal to the resistance (i.e., i). At the same time, the current in the circuit is at its maximum (i.e., ii). Since the reactance of the inductor and capacitor cancel each other out, there is no phase difference between the current and voltage (i.e., iv is not true), so iii is not applicable. Therefore, the correct answer is (a) i and ii only.

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When an object is placed in front of two plane mirrors inclined at an angle to each other, multiple images are formed. The number of images formed can be determined using the formula: N = 360^o / θ - 1 where N is the number of images formed and θ is the angle between the mirrors. In this case, the angle between the mirrors is 60^o, so: N = 360^o / 60^o - 1 N = 6 - 1 N = 5 Therefore, the number of images formed is 5. So, the correct option is (c) 5.

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The apparent cubic expansivity (α) of a liquid is defined as the increase in volume per unit volume per degree rise in temperature. It is given by the formula: α = (1/V) (ΔV/ΔT) where V is the volume of the liquid and ΔV/ΔT is the rate of change of volume with temperature. In this problem, the density bottle has a mass of 30g when empty and 38g when filled with the liquid. Therefore, the mass of the liquid is: mass of liquid = 38g - 30g = 8g Let the volume of the liquid be V. The density of the liquid is given by: density = mass/volume or ρ = m/V The mass and volume of the liquid both change with temperature. However, since the density bottle is made of a material with a negligible expansivity, the change in its volume can be ignored. Therefore, the change in the volume of the liquid is equal to the change in the volume of the density bottle. Let ΔV be the change in volume of the density bottle for a temperature rise of ΔT. Then: α = (1/V) (ΔV/ΔT) = (ΔV/VΔT) The apparent cubic expansivity can be calculated as: α = (ΔV/V) / ΔT To find ΔV/V, we can use the fact that the density of the liquid is equal to its mass per unit volume. Let ρ₀ be the density of the liquid at a temperature of T₀, and let ρ be its density at a temperature of T₀ + ΔT. Then: ΔV/V = (V₂ - V₁)/V₁ = (ρ₁ - ρ₀)/ρ₀ where V₁ and V₂ are the volumes of the liquid at temperatures T₀ and T₀ + ΔT, respectively. Substituting the values given in the problem, we get: ΔV/V = [(8g/V) - (30g/V)] / (30g/V) = -22/30 α = (-22/30) / ΔT We are not given the value of ΔT, so we cannot calculate the exact value of α. However, we can simplify the expression for α as follows: α = (-22/30) / ΔT = (-11/15) / (ΔT/2) Since the answer choices are given in terms of powers of 10, we can rewrite this as: α = (-1.1) x 10^-1 / (ΔT/2) = (-2.2) x 10^-1 / ΔT Comparing this with the answer choices, we see that the correct option is: 6.25 x 10^-3K^-1 Therefore, the apparent cubic expansivity of the liquid is 6.25 x 10^-3K^-1.

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The acceleration of an object can be calculated using the equation: acceleration = (final velocity - initial velocity)/time Since the car starts from rest, its initial velocity is 0. Therefore, we can simplify the equation to: acceleration = final velocity/time We are given that the car covers a distance of 40m in 10s. To find the final velocity, we can use the following equation of motion: distance = (initial velocity * time) + (0.5 * acceleration * time^2) Since the car starts from rest, its initial velocity is 0. Therefore, we can simplify the equation to: distance = 0.5 * acceleration * time^2 Rearranging the equation, we get: acceleration = 2 * distance/time^2 Substituting the given values, we get: acceleration = 2 * 40m / (10s)^2 Simplifying the expression, we get: acceleration = 0.8 m/s^2 Therefore, the magnitude of the car's acceleration is 0.80ms^-2. Answer is the correct answer.

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A compound microscope is an optical instrument that uses two lenses (the objective lens and the eyepiece lens) to produce magnified images of small objects. The objective lens forms a real image of the object that is located inside the focal point of the eyepiece. The eyepiece lens then acts as a magnifying glass to produce a virtual image of the real image formed by the objective lens. The magnification produced by the compound microscope is the product of the magnification produced by each lens. The formula for calculating the magnification of a compound microscope is given as: M = - (f_o / f_e) Where M is the magnification produced by the microscope, f_o is the focal length of the objective lens, and f_e is the focal length of the eyepiece lens. From the formula, we can see that the focal length of the objective lens and the focal length of the eyepiece lens are inversely proportional to the magnification produced by the microscope. As the magnification of the microscope increases, the focal length of the objective lens decreases, and the focal length of the eyepiece lens increases. Therefore, the correct relation between the focal length of the objective lens and the focal length of the eyepiece lens is: f_o < f_e This is because the objective lens is designed to produce a real image of the object, and the eyepiece lens is designed to magnify that image. To achieve a higher magnification, the eyepiece lens must have a shorter focal length than the objective lens.

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The statement "If no net force acts on an object, the object maintains a state of rest or constant speed in a straight line" is a statement of Newton's first law of motion. The first law of motion, also known as the law of inertia, states that an object at rest tends to stay at rest, and an object in motion tends to stay in motion with a constant speed and in a straight line, unless acted upon by a net external force.

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When an object of mass m moves in a circular path of radius r with uniform speed v, it experiences a force towards the center of the circle known as the centripetal force. The magnitude of the centripetal force is given by the formula F = ma, where a is the centripetal acceleration. The centripetal acceleration can be expressed in terms of the angular speed \(\omega\), as a = r\(\omega^2\). Therefore, the magnitude of the centripetal force can be calculated by multiplying the mass of the object by the centripetal acceleration. So, F = ma = m(r\(\omega^2\)) = m\(\omega^2\)r Hence, the correct option is: - \(m \omega^2 r\)

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When a body rests on an inclined plane, its weight can be resolved into two components: one perpendicular to the plane, and the other parallel to the plane. The component of weight parallel to the inclined plane is given by Mg sin \(\theta\), where M is the mass of the body, g is the acceleration due to gravity, and \(\theta\) is the angle of inclination. This is because the weight acts vertically downwards and the component parallel to the plane is given by the weight multiplied by the sine of the angle of inclination. So, the correct option is Mg sin \(\theta\).

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Transverse waves can be distinguished from longitudinal waves based on their direction of oscillation. In a transverse wave, the oscillations are perpendicular to the direction of wave propagation. Examples of transverse waves include water waves, light waves, and electromagnetic waves. On the other hand, in a longitudinal wave, the oscillations are parallel to the direction of wave propagation. Examples of longitudinal waves include sound waves and seismic waves. Therefore, the correct answer is polarization, which is a phenomenon that occurs only in transverse waves, as they can be polarized by passing them through certain filters that allow only waves oscillating in a particular direction to pass through.

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The quality of a note, also known as timbre, depends on its overtones. Overtones are the additional frequencies produced by an object when it vibrates. While the fundamental frequency of a note determines its pitch, it is the presence and relative strength of overtones that give the note its distinctive timbre. Different instruments or voices playing or singing the same note will sound different because of the unique combination of overtones they produce. Amplitude refers to the loudness of a sound, while frequency is the number of vibrations per second and determines the pitch of the sound.

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Principle. An electron moving at speed v perpendicular to a magnetic field B experiences a magnetic force \(qvB\) that provides the centripetal force for its circular orbit:

Substituting \(v = 2.00\times10^{7}\ \text{m/s}\), \(B = 1.20\times10^{-3}\ \text{T}\), \(q = 1.6\times10^{-19}\ \text{C}\), and the electron mass \(m = 9.11\times10^{-31}\ \text{kg}\) (the printed \(10^{-3}\) is a misprint for \(10^{-31}\)):

The radius of the orbit is about 0.095 m (9.5 cm).

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(a) How a gas can be made to conduct electricity

Under normal conditions a gas is a very good insulator because it contains almost no free charge carriers; its molecules are neutral. A gas is made to conduct by ionising it, that is, by knocking electrons out of some of its molecules so that free electrons and positive ions are produced. This is achieved by:

• Applying a very high potential difference (strong electric field) across the gas so that stray electrons are accelerated hard enough to knock electrons out of neutral molecules on collision, causing further ionisation (an ionisation avalanche).
• Reducing the gas pressure (as in a discharge tube). At low pressure the molecules are far apart, so accelerated electrons travel a long free path and gain enough energy between collisions to ionise the gas.
• Ionising the gas by other agents such as X-rays, ultraviolet light, or radiation from radioactive sources, which free electrons from the molecules.

Once ions and free electrons exist, they drift under the applied field and constitute a current, so the gas conducts.

(b) The electric charge carriers in gases

• Negatively charged free electrons (and negative ions).
• Positively charged positive ions (molecules that have lost electrons).

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Using the range formula. For a projectile launched with speed u at angle \(\theta\), the horizontal range is

With \(R = 78\ \text{m}\), \(u = 30\ \text{m/s}\), \(g = 10\ \text{m/s}^{2}\):

The ball is projected at \(\theta \approx \mathbf{30^{\circ}}\) (the complementary angle \(60^{\circ}\) gives the same range).

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(a) Electromotive force (emf)
The electromotive force of a source is the total energy supplied by the source in driving one coulomb of charge round the complete circuit; that is, the work done per unit charge by the source (equal to the terminal potential difference of the source on open circuit). Its SI unit is the volt (V).

(b) Potentiometer
(i) Principle of operation: A steady current is passed through a uniform resistance wire, so the potential difference across a portion of the wire is directly proportional to its length, giving a uniform potential gradient. An unknown emf or p.d. is balanced against the p.d. across a length of the wire; at balance no current flows through the galvanometer (null method), so \( V \propto L \), where \(V\) is the p.d. and \(L\) is the balance length.

(ii) Two advantages of a potentiometer over a voltmeter:

1. At balance it draws no current from the cell being measured, so it measures the true emf and eliminates error due to the internal resistance of the cell (a voltmeter draws current and reads less than the emf).
2. It is more sensitive and more accurate, since it uses a null method and needs no scale calibration that could introduce zero or scale errors.

(c)(i) Labelled sketch of a gold-leaf electroscope:

The metal cap collects charge and passes it down the metal rod to the metal plate and the gold leaf. Because the plate and leaf then carry like charges, the leaf is repelled and diverges from the plate. The rod is held by an insulating plug in the top of an earthed metal case that has glass windows for viewing.

(ii) Use of a gold-leaf electroscope: to detect the presence of electric charge on a body (it can also be used to test the sign of a charge and to compare the magnitudes of charges).

(d)(i) Action of a magnetic relay: A small current in the coil (the control circuit) magnetises a soft-iron core, turning it into an electromagnet. The electromagnet attracts a pivoted soft-iron armature, and the movement of the armature closes (or opens) a pair of contacts in a separate circuit. In this way a small current in the first circuit is used to switch on or off a much larger current in the second circuit.

(ii) Two factors which determine the magnitude of an induced emf in a coil:

1. The rate of change of magnetic flux linkage (the speed at which the flux through the coil changes).
2. The number of turns in the coil.

(iii) Force per unit length on the wire

Given: current \(I = 5\ \text{A}\), flux density \(B = 2.0\times10^{-3}\ \text{T}\), angle to the field \(\theta = 30^{\circ}\).

The force on a current-carrying conductor is \(F = BIL\sin\theta\), so the force per unit length is

The force per unit length exerted on the wire is \(5.0\times10^{-3}\ \text{N m}^{-1}\).

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(a) Heat capacity

The heat capacity of a body is the quantity of heat required to raise the temperature of the whole body by one kelvin (or one degree Celsius). Its SI unit is the joule per kelvin (J K\(^{-1}\)).

(b) Two effects of heat on a substance

• It causes a rise in temperature.
• It causes expansion (increase in size) of the substance.

(Other acceptable effects: change of state, e.g. melting or boiling; change in physical properties such as electrical resistance; chemical change.)

(c) Removing a tightly fitted glass stopper

Warm the neck of the bottle gently (for example with warm water or by rubbing). The glass of the neck, being on the outside, heats up and expands first (before the stopper), so the neck widens slightly. The stopper, still at its original size, becomes loose and can be eased out.

(d) The microwave soup

Data: \(m = 800\text{ g} = 0.8\text{ kg}\), \(\theta_1 = 30^{\circ}\text{C}\), \(P = 1200\text{ W}\), \(t = 3\text{ min} = 180\text{ s}\), \(c = 4000\ \text{J kg}^{-1}\text{K}^{-1}\).

(i) Final temperature

Heat supplied: \(Q = Pt = 1200 \times 180 = 216000\ \text{J}\).

Temperature rise: \(\Delta\theta = \dfrac{Q}{mc} = \dfrac{216000}{0.8 \times 4000} = \dfrac{216000}{3200} = 67.5\ \text{K}\).

\(\theta_2 = 30 + 67.5 = \mathbf{97.5\ ^{\circ}C}\).

(ii) As the soup heats up, water in it turns to steam and the trapped air expands, so the pressure inside a tightly sealed container builds up greatly. Since the lid is tight-fitting, the gas cannot escape; the pressure can burst the container or blow off the lid violently. Hence tight-fitting lids are unsafe in microwave cooking.

(iii) On cooling, the hot vapour inside condenses and the trapped gas contracts, so the pressure inside the sealed container falls below the atmospheric pressure outside. The greater external atmospheric pressure then pushes the walls of the plastic container inward, producing the observed dent.

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(a) Einstein's photoelectric equation

\[ hf = W_{0} + \tfrac{1}{2}mv_{\max}^{2} \]

• \(hf\) = energy of the incident photon (\(h\) = Planck constant, \(f\) = frequency of the incident light).
• \(W_{0}\) = work function of the metal (minimum energy to free an electron from the surface).
• \(\tfrac{1}{2}mv_{\max}^{2}\) = maximum kinetic energy of the emitted photoelectron.

(b) Factors for a photocell

• (i) Emission: the frequency of the incident light must be at or above the threshold frequency (photon energy at least equal to the work function).
• (ii) Rate of emission: the intensity (brightness) of the incident light (number of photons arriving per second).
• (iii) Energy of photoelectrons: the frequency of the incident light (and the work function of the metal).

(c)(i) Nuclear equations

Equation A: \(^{222}_{p}\text{Rn} \to\ ^{218}_{84}\text{Po} +\ ^{q}_{2}\text{He}\). Balancing charge: \(p = 84 + 2 = 86\). Balancing mass: \(q = 222 - 218 = 4\). So \(p = 86\), \(q = 4\) (an alpha particle is emitted).

Equation B: \(^{214}_{83}\text{Bi} \to\ ^{214}_{84}\text{Po} +\ ^{m}_{n}\text{X}\). Balancing mass: \(m = 214 - 214 = 0\). Balancing charge: \(n = 83 - 84 = -1\). So \(m = 0\), \(n = -1\), and X is a beta particle (electron), \(^{0}_{-1}e\).

(ii) Radioactive waste emits ionising radiation that is harmful to living cells (it can cause cancer, genetic damage and death) and can persist for a long time, so it must be disposed of safely to protect people and the environment from radiation exposure.

(d)(i) Energy of the photon

\(E = \dfrac{hc}{\lambda} = \dfrac{6.6\times10^{-34}\times3.0\times10^{8}}{2.4\times10^{-7}} = \dfrac{19.8\times10^{-26}}{2.4\times10^{-7}} = 8.25\times10^{-19}\ \text{J}\).

This corresponds to the option \(8.2\times10^{-19}\ \text{J}\).

(ii) On the energy-level diagram, the photon of energy \(8.2\times10^{-19}\ \text{J}\) is emitted when the atom makes a downward transition (electron falling) between the two levels whose energy difference equals \(8.2\times10^{-19}\ \text{J}\); the arrow is drawn pointing downwards from the higher to the lower of those two levels. The exact levels can only be marked on the actual figure provided.

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The straight-line graph is a plot of the maximum kinetic energy \(E_k\) of the emitted electrons (vertical axis) against the frequency \(f\) of the radiation falling on the metal surface (horizontal axis). It obeys Einstein's photoelectric equation:

where \(h\) is Planck's constant, \(W_0\) is the work function of the metal and \(f_0\) is the threshold frequency. Comparing this with the equation of a straight line \(y = mx + c\) lets each feature of the graph be interpreted directly, as annotated below.

(a) Slope of the graph

The line has the form \(E_k = hf - hf_0\). Matching term by term with \(y = mx + c\), the gradient \(m\) corresponds to \(h\). Therefore

The slope of the graph represents Planck's constant \(h\). Because \(h\) is a universal constant, the graph has the same gradient for every metal.

(b) Intercept, OC

Point C is where the line, produced backwards, cuts the energy axis at \(f = 0\). Substituting \(f = 0\) into the equation gives

The intercept OC is therefore negative, and its magnitude equals the work function \(W_0 = hf_0\) of the metal, i.e. \(OC = hf_0 = W_0\). This is the minimum energy needed to free an electron from the metal surface.

(c) Intercept, OK

Point K is where the line crosses the frequency axis at \(E_k = 0\). Setting \(E_k = 0\):

The intercept OK represents the threshold (cut-off) frequency \(f_0\) of the incident radiation: the minimum frequency below which no electrons are emitted from the surface, however intense the radiation.

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Vertical motion (to find time of flight). The particle is projected horizontally, so its initial vertical velocity is zero. Falling a height \(h = 20\ \text{m}\):

Horizontal motion (constant velocity). Horizontal speed \(u = 10\ \text{m/s}\), so the horizontal distance (range) is

The particle strikes the ground 20 m from the foot of the tower.

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Definition. Young's modulus is the ratio of tensile stress to tensile strain within the elastic limit:

Convert the data.

• Original length \(L = 50\ \text{cm} = 0.50\ \text{m}\)
• Cross-sectional area \(A = 4.0\ \text{cm}^{2} = 4.0\times10^{-4}\ \text{m}^{2}\)
• Force \(F = 35\ \text{kN} = 35\,000\ \text{N}\)
• Extension \(e = 0.25\ \text{mm} = 2.5\times10^{-4}\ \text{m}\)

Substitute.

Young's modulus of the bar is \(1.75\times10^{11}\ \text{Pa}\) (N m\(^{-2}\)).

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