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The diagram above illustrates a structure of a typical photocell.
(i) Identify each of the parts labelled A and B.
(ii) State one function each of A and B.
(iii) Einstein’s photoelectric equation can be written as \(E = hf - W_o\). State what each of the terms \(E\), \(hf\) and \(W_o\) represent.
(b) A photon is incident on a metal whose work function is \(1.32\ \text{eV}\). An electron is emitted from the surface with a maximum kinetic energy of \(1.97\ \text{eV}\). Calculate the frequency of the photon. \([1\ \text{eV} = 1.6 \times 10^{-19}\ \text{J}]\)
(c)(i) Define half-life of a radioactive element.
(ii) Sketch a graph of the relation \(N = N_0e^{-\lambda t}\) and indicate the half-life.
(a)(i) Parts of the photocell (standard evacuated photocell): A is the photocathode (emitter) - a curved metal plate coated with a photosensitive material. B is the anode (collector) - a small metal rod or ring placed in front of the cathode.
(a)(ii) Functions: A (photocathode) emits electrons when light of sufficient frequency falls on it. B (anode) collects the emitted photoelectrons, so completing the circuit and allowing a photocurrent to flow.
(a)(iii) Terms in Einstein's equation \(E = hf - W_0\): \(E\) is the maximum kinetic energy of the emitted photoelectron; \(hf\) is the energy of the incident photon (h = Planck's constant, f = frequency); \(W_0\) is the work function, the minimum energy needed to release an electron from the metal surface.
(b) Frequency of the photon: Photon energy \(= KE_{max} + W_0 = 1.97 + 1.32 = 3.29\,\text{eV}\).
\[ E = 3.29\times1.6\times10^{-19} = 5.264\times10^{-19}\,\text{J}. \]
\[ f = \frac{E}{h} = \frac{5.264\times10^{-19}}{6.6\times10^{-34}} \approx 7.98\times10^{14}\,\text{Hz}. \]
(c)(i) Half-life: The half-life of a radioactive element is the time taken for half the atoms (nuclei) originally present in a sample to decay.
(c)(ii) Graph of \(N = N_0 e^{-\lambda t}\): Plot \(N\) (number of undecayed nuclei) on the vertical axis against time \(t\). The curve starts at \(N_0\) and falls exponentially towards zero. The half-life \(t_{1/2}\) is read on the time axis at the point where \(N = N_0/2\).
(a)(i) Parts of the photocell (standard evacuated photocell): A is the photocathode (emitter) - a curved metal plate coated with a photosensitive material. B is the anode (collector) - a small metal rod or ring placed in front of the cathode.
(a)(ii) Functions: A (photocathode) emits electrons when light of sufficient frequency falls on it. B (anode) collects the emitted photoelectrons, so completing the circuit and allowing a photocurrent to flow.
(a)(iii) Terms in Einstein's equation \(E = hf - W_0\): \(E\) is the maximum kinetic energy of the emitted photoelectron; \(hf\) is the energy of the incident photon (h = Planck's constant, f = frequency); \(W_0\) is the work function, the minimum energy needed to release an electron from the metal surface.
(b) Frequency of the photon: Photon energy \(= KE_{max} + W_0 = 1.97 + 1.32 = 3.29\,\text{eV}\).
\[ E = 3.29\times1.6\times10^{-19} = 5.264\times10^{-19}\,\text{J}. \]
\[ f = \frac{E}{h} = \frac{5.264\times10^{-19}}{6.6\times10^{-34}} \approx 7.98\times10^{14}\,\text{Hz}. \]
(c)(i) Half-life: The half-life of a radioactive element is the time taken for half the atoms (nuclei) originally present in a sample to decay.
(c)(ii) Graph of \(N = N_0 e^{-\lambda t}\): Plot \(N\) (number of undecayed nuclei) on the vertical axis against time \(t\). The curve starts at \(N_0\) and falls exponentially towards zero. The half-life \(t_{1/2}\) is read on the time axis at the point where \(N = N_0/2\).
