Maharashtra Board Solutions for Chapter: Structure of Atoms and Nuclei, Exercise 3: Exercises

Calculate the energy released in the nuclear reaction ${}_3{}^7\mathrm{Li} + \mathrm{p} \to 2\mathrm{\alpha }$ given mass of ${}_3{}^7\mathrm{Li}$ atom and of helium atom to be $7.016 \mathrm{u}$ and $4.0026 \mathrm{u}$ respectively. Mass of a proton is $1.00728 \mathrm{u}$.

Sample of carbon obtained from any living organism has a decay rate of $15.3$ decays per gram per minute. A sample of carbon obtained from very old charcoal shows a disintegration rate of $12.3$ disintegrations per gram per minute. Determine the age of the old sample given the decay constant of carbon to be $3.839\times {10}^{-12}$ per second.

The half-life of ${}_{38}{}^{90}\mathrm{Sr}$ is $28$ years. Determine the disintegration rate of its $5 \mathrm{mg}$ sample.

What is the amount of ${}_{27}{}^{60}\mathrm{Co}$ necessary to provide a radioactive source of strength $10.0 \mathrm{mCi}$, its half-life being $5.3$ years?

Disintegration rate of a sample is ${10}^{10}$ per hour at $20$ hours from the start. It reduces to $6.3\times {10}^9$ per hour after $30$ hours. Calculate its half life and the initial number of radioactive atoms in the sample.

A source contains two species of phosphorous nuclei, ${}_{15}{}^{32}\mathrm{P} \left({\mathrm{T}}_{\frac{1}{2}}=14.3 \mathrm{d}\right)$ and ${}_{15}{}^{33}\mathrm{P} \left({\mathrm{T}}_{\frac{1}{2}}=25.3 \mathrm{d}\right)$. At time $t=0, 90\%$ of the decays are from ${}_{15}{}^{32}\mathrm{P}$. How much time has to elapse for only $15\%$ of the decays to be from ${}_{15}{}^{32}\mathrm{P}$?

How much mass of ${}^{235}\mathrm{U}$ is required to undergo fission each day to provide $3000 \mathrm{MW}$ of thermal power? Average energy per fission is $202.79 \mathrm{MeV}$

In a periodic table the average atomic mass of magnesium is given as $24.312 \mathrm{u}$. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are${}_{12}{}^{24}\mathrm{Mg} (23.98504 \mathrm{u})$,${}_{12}{}^{25}\mathrm{Mg} (24.98584 \mathrm{u})$ and ${}_{12}{}^{26}Mg (25.98259 \mathrm{u})$. The natural abundance of ${}_{12}{}^{24}\mathrm{Mg}$ is $78.99\%$  by mass. Calculate the abundances of other two isotopes.