Chapter 4

\begin{aligned} &\text { How many } \alpha-\text { and } \beta \text { -particles will be emitted when }{ }_{90} \mathrm{Th}^{232} \text { changes }\\\ &\text { into }{ }_{82} \mathrm{~Pb}^{208} \text { ? } \end{aligned}

Give one example each of (a) \(\alpha\) -emission, (b) \(\beta^{+}\) -emission, and (c) K-capture. Write the equation for these nuclear changes.

Complete the following nuclear reactions : (a) \({ }_{42}^{~} \mathrm{Mo}(\ldots, n){ }_{43}^{97} \mathrm{Tc}\) (b) .... \((\alpha, 2 n) \stackrel{211}{85} \mathrm{At}\) (c) \({ }_{25}^{55} \mathrm{Mn}(n, \gamma) \ldots\) (d) \({ }_{96}^{246} \mathrm{Cm}+{ }_{6}^{12} \mathrm{C} \longrightarrow \ldots .+4_{0}^{1} n\) (e) \({ }_{13}^{27} \mathrm{Al}(\alpha, n) \ldots\) (f) \({ }_{92}^{215} \mathrm{U}\left(\alpha, \beta^{-}\right) \ldots\)

The half life of \(_{38} \mathrm{Sr}^{90}\) is 20 year. If the sample of this nucleide has an activity of 8,000 disintegrations \(\min ^{-1}\) today, what will be its activity after 80 year?

A sample of wooden air craft is found to undergo 9 dpm \(g^{-1}\) of \(C^{14}\). What is approximate age of air craft? The half life of \(_{6} \mathrm{C}^{14}\) is 5730 year and rate of disintegration of wood recently cut down is 15 dpm \(\mathrm{g}^{-1}\) of \(_{6} \mathrm{C}^{14} ?\)

A piece of wood from an archeological source shows a \({ }^{14} \mathrm{C}\) activity which is \(60 \%\) of the activity found in fresh wood today. Calculate the age of the archeological sample. \(\left(t_{1 / 2}{ }^{14} \mathrm{C}=5770\right.\) year \()\)

The \(\beta^{-}\) -activity of a sample of \(\mathrm{CO}_{2}\) prepared from a contemporary wood gave a count rate of \(25.5\) counts per minute (c.p.m.). The same mass of \(\mathrm{CO}_{2}\) from an ancient wooden statue gave a count rate of \(20.5 \mathrm{cpm} .\), in the same counter condition. Calculate its age to the nearest 50 year taking \(t_{1 / 2}\) for \({ }^{14} \mathrm{C}\) as 5770 year. What would be the expected count rate of an identical mass of \(\mathrm{CO}_{2}\) from a sample which is 4000 year old?

A \(0.2 \mathrm{~mL}\) sample of a solution containing \(1.0 \times 10^{-7}\) curie of \(_{1} \mathrm{H}^{3}\) is injected to the blood stream of an animal. After sufficient time for circulatory equilibrium to be established, \(0.10 \mathrm{~mL}\) of blood is found to have an activity of \(20 \mathrm{dpm}\). Calculate the volume of blood in animal, assuming no change in activity of sample during criculatory equilibrium.

Calculate the density of the nucleus of \(_{47} \mathrm{Ag}^{107}\) assuming \(r_{\text {nucleus }}\) is \(1.4 A^{1 / 3} \times 10^{-13} \mathrm{~cm} .\) Where \(A\) is mass number of nucleus. Compare its density with density of metallic silver \(10.5 \mathrm{~g} \mathrm{~cm}^{-3}\).