(a) Explain the terms: (i) transmutation as it relates to radioactivity; (ii) stopping potential. (b) \(^{23}_{11}A + ^2_1B\) —> \(^p_qC\) + proton \(^p_qC\...

(a)(i) Transmutation: Transmutation is the change of one element into another as a result of a nuclear reaction, in which the number of protons in the nucleus (the atomic number) changes, for example during radioactive decay or artificial nuclear bombardment.

(a)(ii) Stopping potential: The stopping potential is the minimum negative (retarding) potential that must be applied to the collecting electrode of a photocell to just stop the most energetic photoelectrons from reaching it, so that the photocurrent becomes zero. \(eV_s = KE_{max}\).

(b) Nuclear equations:

\[ {}^{23}_{11}A + {}^{2}_{1}B \rightarrow {}^{p}_{q}C + {}^{1}_{1}\text{(proton)}. \]

Conserving nucleon number: \(23 + 2 = p + 1 \Rightarrow p = 24\). Conserving charge: \(11 + 1 = q + 1 \Rightarrow q = 11\).

\[ {}^{24}_{11}C \rightarrow {}^{r}_{s}E + {}^{0}_{-1}\beta. \]

Conserving nucleon number: \(24 = r + 0 \Rightarrow r = 24\). Conserving charge: \(11 = s + (-1) \Rightarrow s = 12\).

Therefore \(p = 24,\; q = 11,\; r = 24,\; s = 12\).

(c) Energy of the incident photon:

\[ E = \frac{hc}{\lambda} = \frac{(6.6\times10^{-34})(3.0\times10^{8})}{3.6\times10^{-7}} = 5.5\times10^{-19}\,\text{J}. \]

Work function \(W_0 = 1.6\,\text{eV} = 1.6\times(1.6\times10^{-19}) = 2.56\times10^{-19}\,\text{J}\).

(i) Maximum kinetic energy:

\[ KE_{max} = E - W_0 = 5.5\times10^{-19} - 2.56\times10^{-19} = 2.94\times10^{-19}\,\text{J}. \]

(ii) Speed of the emitted electron: from \(KE = \tfrac{1}{2}mv^{2}\),

\[ v = \sqrt{\frac{2\,KE}{m}} = \sqrt{\frac{2\times2.94\times10^{-19}}{9.1\times10^{-31}}} = \sqrt{6.46\times10^{11}} \approx 8.04\times10^{5}\,\text{m s}^{-1}. \]

(d) Moving the source of ultra-violet light farther from the metal only reduces the intensity (number of photons per second arriving), so fewer electrons are emitted per second. It does not change the frequency/energy of each photon, so the maximum kinetic energy and hence the maximum speed of the ejected electron remain unchanged.