IBDP Physics- E.1 Structure of the atom- IB Style Questions For HL Paper 2 -FA 2025
▶️ Answer/Explanation
(a)
(i) At sufficiently high energies, the alpha particle approaches the nucleus closely enough for the strong nuclear force to act. This short-range attractive force is not included in the Rutherford model, which assumes only electrostatic repulsion.
(ii) At the threshold energy \(E_{0}\), the distance of closest approach of the alpha particle is approximately equal to the nuclear radius. By equating the initial kinetic energy to the electric potential energy at closest approach, \(E_{0} = \frac{kQq}{r}\), the value of \(r\) (the nuclear radius) can be estimated.
(b)
(i) The half-life in seconds is \(T_{\frac{1}{2}} = 2.69 \times 24 \times 3600 \approx 2.32 \times 10^{5}\,s\).
The decay constant is \(\lambda = \frac{\ln 2}{T_{\frac{1}{2}}} \approx \frac{0.693}{2.32 \times 10^{5}} = 2.98 \times 10^{-6}\,s^{-1}\).
(ii) After one week (\(t = 7 \times 24 \times 3600 = 6.05 \times 10^{5}\,s\)), the remaining mass of Au-198 is \(m = m_{0}e^{-\lambda t} \approx 5.0e^{-1.80} \approx 0.82\,mg\).
The mass of Hg-198 formed is therefore \(5.0 – 0.82 \approx 4.2\,mg\).
(c)
The gamma photons are emitted with specific, well-defined frequencies. Using \(E = hf\), each frequency corresponds to a particular energy difference between nuclear states. Since only certain photon energies are observed, this shows that nuclei can exist only in specific energy states, providing evidence that nuclear energy levels are discrete.