Embibe Experts Solutions for Chapter: Nuclei, Exercise 1: Meghalaya-2018

What is half-life of a radioactive nucleus? Show that half-life is inversely proportional to the decay constant of the radioactive sample.

Find the binding energy per nucleon of an a-particle in $\mathrm{MeV}$. (Take,$1 \mathrm{a}.\mathrm{m}.\mathrm{u}.= 931.5 \mathrm{MeV}$ ) Given-

mass of $\alpha$-particle$=4.00150 \mathrm{a}.\mathrm{m}.\mathrm{u}.$

mass of proton$=1.00728 \mathrm{a}.\mathrm{m}.\mathrm{u}.$

mass of neutron$=1.00867 \mathrm{a}.\mathrm{m}.\mathrm{u}.$

What are isotones?

$A\stackrel{\alpha }{\to }{A}_1\stackrel{\beta }{\to }{A}_2\stackrel{\alpha }{\to }{A}_3$

The mass number and atomic number of $A$ are $180$ and $72$ respectively. What are these numbers for $A_3$?

State radioactive decay law. Derive the relation $N=N_0{e}^{-\lambda t}$, where symbols have their usual meanings.

What is a chain reaction ?

From the law of radioactive decay, show that the total rate of decay, $R=R_0{e}^{-\lambda t}$, where the symbols have their usual meanings.

Derive the relationship between half-life of a radioactive substance and its decay constant.