(a) (i) What is nuclear fission? (ii) State the function of each of the following ma-terials in a nuclear fision reactor: (\(\alpha\)) graphite, (\(\beta\))...
Question 1 Report
(a) (i) What is nuclear fission?
(ii) State the function of each of the following ma-terials in a nuclear fision reactor:
(\(\alpha\)) graphite, (\(\beta\)) boron rods; (\(\gamma\)) liquid sodium
(b) The table below gives some of the energy levels of a hydrogen atom.
| n | 1 | 2 | 3 | 4 | 5 | \(\infty\) |
| \(E_n/\text{eV}\) | -13.60 | -3.39 | -1.51 | -0.85 | -0.54 | 0.00 |
(i) Draw the energy level diagram for the atom.
(ii) Determine the wavelength of the photon emitted when the atom goes from the energy state \(n = 3\) to the ground state. [\(h = 6.6 \times 10^{-34}\,\mathrm{Js}\), \(c = 3 \times 10^{8}\,\mathrm{ms}^{-1}\), \(e = 1.6 \times 10^{-19}\)]
(c) A piece of ancient bone from an excavation site showed \(^{14}_{6}\mathrm{C}\) activity of 9.5 disintegrations per minute per \(1.0 \times 10^{-3}\,\mathrm{kg}\). If a bone specimen from a living creature shows \(^{14}_{6}\mathrm{C}\) activity of 12.0 disintegrations per minute per \(1.0 \times 1 0^{-3}\), determine the age of the ancient bone. [Half - life of \(^{14}_{6}\mathrm{C} = 5572\) years].
Answer Details
(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
| Material | Function |
|---|---|
| Graphite | It acts as a moderator, slowing down fast neutrons so that they can cause further fission. |
| Boron rods | They absorb excess neutrons and hence control the rate of the chain reaction. |
| Liquid sodium | It acts as a coolant, removing heat from the reactor core. |
(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 \(\boxed{1878\ \text{years}}\).
Download The App On Google Playstore
Everything you need to excel in your exams
