The correct answer is D because:

The nucleus ${}_{Z}^{A}X$ has an atomic number Z and a mass number A
- Therefore, the nucleus has Z number of protons and (A–Z) number of neutrons
In terms of the masses of each nucleon:
- The total mass of constituent protons is given by $Z m_{p}$
- The total mass of constituent neutrons is given by $(A - Z) m_{n}$
- Therefore, the mass of constituent nucleons = $Z m_{p} + (A - Z) m_{n}$
The mass defect of this nucleus Δm = mass of constituent nucleons – mass of the nucleus
- Δm = ( $Z m_{p} + (A - Z) m_{n}$ ) – M
The binding energy ΔE = Δmc²
- Therefore ΔE = (( $Z m_{p} + (A - Z) m_{n}$ ) – M)c²
Therefore, the binding energy per nucleon is the binding energy divided by the number of nucleons
- The number of nucleons is given by the mass number, A
Therefore, $\frac{∆ E}{A} = \frac{(Z m_{p} + (A - Z) m_{n} - M) c^{2}}{A} = (\frac{Z m_{p} + (A - Z) m_{n} - M}{A}) c^{2}$

Even though this question may look scary at first, it actually provides you with really good practice to recognise and use numbers like the mass number A, the atomic number (number of protons) Z, and the number of neutrons therefore being the difference between the two, A–Z. Once you have these three pieces of information, along with the mass of a nucleus, the first step is always to calculate a mass defect Δm, which is the difference between the mass of the constituent nucleons and the mass of them joined together in a nucleus.

	Controlling	Moderating
A	boron	water
B	boron	cadmium
C	carbon	cadmium
D	carbon	water

Nuclear Fusion & Fission (AQA A Level Physics)

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