(a) Write Einstein's photoelectric equation and identh: each component of the equation.
(b) For a photocell, star; one factor each that is responsible fo: the:
(i) emission (ii) rate of emission;
(iii) energy of photoelectrons.
(c)(i) Two nuclear equations are given below:
\(^{222}_{p}RN\) \(\to\) \(^{218}_{84}PO + ^q_2He\)...................A
\(^{214}_{83}RN\) \(\to\) \(^{214}_{84}PO + ^m_nX\)...................B
Determine the values of: (\(\alpha\)) p and q in equation A; (\(\beta\)) in and n in equation B and identify X.
(ii) Give a reason why it is important to dispose o radioactive waste safely.
(d)(i) A certain atom emits ultra violet photon of wavelength 2.4 x10\(^{-7}\)m. Calculate the energy of the photon:
----------------- - 6.0 x 10\(^{-19}\)J
---------------- - 8.2 x 10\(^{-19}\)J
---------------- - 8.8 x 10\(^{-19}\)J
---------------- - 16.7 x 10\(^{-19}\)J
(ii) The figure above illustrates the energy levels o the atom. Copy the figure in your answer booklet anc indicate on it, the energy level transitions which cause the emission of the photon in (d)(i) above. [h= 6.6 x 10\(^{-34}\) Js; c = 3.0 x 108 ms\(^{-1}\)].
(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.
(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.
