(a)(i) State the principal factor that determines the relative stability of a radioactive nucleus.
(ii) Arrange the following radioactive nucleus in decreasing order of stability. Justify your answer: X,W and Y:
\(\displaystyle {}^{40}_{20}X \quad {}^{920}_{36}Y \text{ and } {}^{95}_{42}Z\)
(b)(i) Explain the term ionization potential.
(ii)
The diagram above illustrates energy levels in the hydrogen atom. E, is the energy of the \(E_0\) ground state.
(i) When an electron makes a transition from level n = 3 to level n = 1, it emits a photon of wavelength \(1.02 \times 10^{-7}\,\text{m}\). Calculate \(E_0\).
(ii) Calculate the ionization potential of the hydrogen atom.
(c)(i) Explain the statement, the work function of sodium is 2.0 eV. (ii) Light of wavelength 160 mm is shone on the surface of a sodium metal of work function 2.0 eV. Determine whether photoelectrons will be emitted. [\(h = 6.6 \times 10^{-34}\,\text{Js}\), \(e = 3.0 \times 10^{8}\,\text{m/s}\), I eV = \(1.6 \times 10^{-19}\,\text{J}\)]
(a)(i) The stability of a radioactive nucleus is determined by its neutron to proton ratio. If the ratio is too high or too low, the nucleus will become unstable and undergo decay. The relative stability of a nucleus is also influenced by the binding energy per nucleon, which is the energy required to separate the nucleus into its individual protons and neutrons.
(ii) To determine the order of stability of the given nuclei, X, W and Y, we need to examine their neutron to proton ratios. However, the information given is not enough to do so. We need to know the atomic numbers of these nuclei.
(b)(i) Ionization potential refers to the minimum amount of energy required to remove an electron from an atom or ion.
(ii) Information given is not enough to answer the question.
(c)(i) Work function is the minimum amount of energy required to remove an electron from a solid surface. In this case, the work function of sodium is 2.0 eV, meaning that 2.0 eV of energy is required to remove an electron from the surface of a sodium metal.
(ii) The energy of light can be calculated using the formula E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the light. The energy of the light in this case is 1.97 eV. If the energy of the light is greater than the work function of sodium, which is 2.0 eV, photoelectrons will be emitted. In this case, the energy of the light is not enough to remove electrons from the surface of sodium, so photoelectrons will not be emitted.
(a)(i) The stability of a radioactive nucleus is determined by its neutron to proton ratio. If the ratio is too high or too low, the nucleus will become unstable and undergo decay. The relative stability of a nucleus is also influenced by the binding energy per nucleon, which is the energy required to separate the nucleus into its individual protons and neutrons.
(ii) To determine the order of stability of the given nuclei, X, W and Y, we need to examine their neutron to proton ratios. However, the information given is not enough to do so. We need to know the atomic numbers of these nuclei.
(b)(i) Ionization potential refers to the minimum amount of energy required to remove an electron from an atom or ion.
(ii) Information given is not enough to answer the question.
(c)(i) Work function is the minimum amount of energy required to remove an electron from a solid surface. In this case, the work function of sodium is 2.0 eV, meaning that 2.0 eV of energy is required to remove an electron from the surface of a sodium metal.
(ii) The energy of light can be calculated using the formula E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the light. The energy of the light in this case is 1.97 eV. If the energy of the light is greater than the work function of sodium, which is 2.0 eV, photoelectrons will be emitted. In this case, the energy of the light is not enough to remove electrons from the surface of sodium, so photoelectrons will not be emitted.
