(a) (i) What is nuclear fission? (ii) State the function of each of the following ma-terials in a nuclear fision reactor: (\(\alpha\)) graphite, (\(\beta\))...

(a) (i) Nuclear fission is the splitting of a heavy atomic nucleus into two lighter nuclei, with the release of a large amount of energy and neutrons.

(ii) Functions of materials in a nuclear fission reactor

(b) (i) Energy-level diagram of the hydrogen atom:

(ii) For the transition from \(n=3\) to the ground state \(n=1\),

\[\Delta E=E_3-E_1=(-1.51)-(-13.60)=12.09\ \text{eV}\]

\[\Delta E=12.09\times1.6\times10^{-19}=1.9344\times10^{-18}\ \text{J}\]

Using \(\Delta E=\dfrac{hc}{\lambda}\),

\[\lambda=\frac{hc}{\Delta E}=\frac{(6.6\times10^{-34})(3.0\times10^8)}{1.9344\times10^{-18}}\]

\[\lambda=1.02\times10^{-7}\ \text{m}\]

The wavelength of the emitted photon is \(\boxed{1.02\times10^{-7}\ \text{m}}\), or \(102\ \text{nm}\).

(c) The activity is proportional to the number of undecayed carbon-14 nuclei. Thus,

\[\frac{A}{A_0}=\frac{9.5}{12.0}=e^{-\lambda t}\]

\[\lambda=\frac{0.693}{5572}=1.244\times10^{-4}\ \text{year}^{-1}\]

\[t=\frac{1}{\lambda}\ln\left(\frac{A_0}{A}\right)=\frac{1}{1.244\times10^{-4}}\ln\left(\frac{12.0}{9.5}\right)\]

\[t=1.88\times10^3\ \text{years}\]

Therefore, the age of the ancient bone is \(\boxed{1.88\times10^3\ \text{years}}\), approximately \(\boxed{1878\ \text{years}}\).