Suggest why de Broglie’s hypothesis is not consistent with Bohr’s conclusion that the electron’s orbit in the hydrogen atom has a well defined radius.

Estimate, using the graph, the radius of a carbon-12 nucleus.

The ratio $\frac{\text{volume of a nucleaus of mass number }A}{\text{volume of a nucleon}}$ is approximately A.

Comment on this observation by reference to the strong nuclear force.

Estimate, in Bq, the initial activity of the sample.

Calculate, in hours, the time at which the activity of the sample has decreased to one-third of the initial activity.

«de Broglie’s hypothesis states that the» electron is represented by a wave ✔

therefore it cannot be localized/it is spread out/it does not have a definite position ✔

Award MP1 for any mention of wavelike property of an electron.

«$d\sin \theta =\lambda \Rightarrow$» $d=\frac{1.6\times {10}^{-15}}{\sin {17}^{\circ }}/5.47\times {10}^{-15}$ «m» ✔

$R=\frac{d}{2}\approx 2.7/2.8\times {10}^{-15}$ «m» ✔

this implies that the nucleons are very tightly packed/that there is very little space in between the nucleons ✔

because the nuclear force is stronger than the electrostatic force ✔

number of nuclei is $\frac{28\times {10}^{-3}}{64}\times 6.02\times {10}^{23}/2.63\times {10}^{20}$ ✔

$A=$«$\lambda N=2.63\times {10}^{20}\times \frac{5.5\times {10}^{-2}}{3600}$» $4.0\times {10}^{15}$ «Bq» ✔

$\frac{\text{1}}{\text{3}}=e^{-\lambda t}$ ✔

t = 20«hr» ✔

This question could have simply asked for the differences but did not puzzle the students who, when scoring, referred successfully to the differences between Bohr's postulate and de Broglie quantification of the wave like characteristics. Examiners marked this question without reference to particular physicist or what individuals suggested. As a result many scored the first mark for suggesting that electrons have wave like properties. The rest of the answers then commonly restated the stem of the question about a well-defined radius.

Many candidates answered this well but calculated the diameter rather than the radius.

Many scored the first mark but it was rare to see answers that talked about the strong nuclear and electrostatic forces.

Many scored the first mark for calculating the number of nuclei but neglected to convert λ to s^-1.

This was very well answered with the majority of candidates scoring full marks. This is a good indication that candidates weren’t short of time in this paper.