Problem structure
(a) 2, numerical, nuclear radius calculation.
(b) 3, numerical, nuclear density calculation.
(c) 4, numerical, conservation of energy and electrostatics.
(d) 3, qualitative, properties of the strong nuclear force.
(e) 3, numerical/qualitative, nuclear equations and isotopes.
Plan your route before writing. Use equations, diagrams, units, and a clear final justification where needed.
A researcher is investigating the properties of a specific isotope of Gold, $^{197}_{79}\text{Au}$. In a scattering experiment, alpha particles ($^{4}_{2}\text{He}$) are fired at a thin gold foil.
(a)
2 marks
Calculate the radius of a $^{197}_{79}\text{Au}$ nucleus. Assume the constant $r_0 = 1.2 \times 10^{-15} \text{ m}$.
(b)
3 marks
Calculate the mean density of the gold nucleus. Assume the mass of a nucleon is $1.67 \times 10^{-27} \text{ kg}$.
(c)
4 marks
An alpha particle is fired directly towards the centre of a stationary gold nucleus. It has an initial kinetic energy of $8.0 \times 10^{-13} \text{ J}$ when it is very far from the nucleus. Calculate the distance of closest approach to the gold nucleus. Assume the gold nucleus remains stationary and treat both as point charges.
Permittivity of free space $\epsilon_0 = 8.85 \times 10^{-12} \text{ F m}^{-1}$; Elementary charge $e = 1.60 \times 10^{-19} \text{ C}$.
(d)
3 marks
The strong nuclear force is responsible for holding the nucleons together. Describe how the magnitude and nature of the strong nuclear force change as the separation between two nucleons increases from $0.1 \text{ fm}$ to $5.0 \text{ fm}$.
(e)
3 marks
If the gold nucleus were to capture a thermal neutron to become $^{198}_{79}\text{Au}$, and this isotope then underwent $\beta^{-}$ decay, identify the proton number, nucleon number, and the name of the resulting daughter nucleus.
