Embibe Experts Solutions for Chapter: Nuclear Physics, Exercise 2: Exercise - 2

The half-life of $40 \mathrm{K}$ is $T=1.30\times {10}^9 \mathrm{y}$. A sample of $m=1.00 \mathrm{g}$ of pure $\mathrm{KCI}$ gives $c=480 \mathrm{counts} {\mathrm{s}}^{-1}$. If the relative percentage abundance of $40 \mathrm{K}$ (fraction of $40 \mathrm{K}$  present in terms of number of atoms) in natural potassium is $n\times {10}^{–2}\%$ then value of $n$(Answer to the nearest integer). Molecular weight of $\mathrm{KCl}$ is $M=74.5$, Avogadro's number $N_A=6.02\times {10}^{23}, 1y=3.15\times {10}^7 \mathrm{s}$.

If a nucleus ${}_Z{}^{A}x$ emits one $\alpha$-particle and one $\beta$ (negative $\beta$) particle in succession, then the daughter nucleus will have which of the following configurations?

The heavier stable nuclei tend to have a larger $\frac{\mathrm{N}}{\mathrm{Z}}$ ratio because

A ${\mathrm{U}}^{238}$ sample of mass $1.0 \mathrm{g}$ emits alpha particles at the rate $1.24\times {10}^4$ particles per second. $\left(N_A=6.023\times {10}^{23}\right)$

A nitrogen nucleus ${}_7\mathrm{N}^{14}$ absorbs a neutron and can transform into a lithium nucleus ${}_3\mathrm{Li}^7$ under suitable conditions, after emitting

The decay constant of a radioactive substance is $0.173 {\left(\mathrm{years}\right)}^{-1}$. Therefore,

Let $m_p$ be the mass of a proton, $m_n$ the mass of a neutron, $M_1$ the mass of a ${}_{10}{}^{20}\mathrm{Ne}$ nucleus and $M_2$ the mass of a ${}_{20}{}^{40}\mathrm{Ca}$ nucleus. Then

Nuclei of the radioactive element $A$ are being produced at a constant rate $\alpha$. The element has a decay constant $\lambda$. At the time $t=0$, there are $N_0$ nuclei of the element.