Embibe Experts Solutions for Chapter: Atoms and Nuclei, Exercise 2: Level 2

A radioactive material decays by simultaneous emissions of two particles with half lives of $1400$ years and $700$ years, respectively. What will be the time after the which one third of the material remains ? (Take $\ln 3=1.1$)

The half-life of ${}^{198}\mathrm{Au}$ is $3$ days. If atomic weight of ${}^{198}\mathrm{Au}$ is $198 \mathrm{g} {\mathrm{mol}}^{-1}$, then the activity of $2 \mathrm{mg}$ of ${}^{198}\mathrm{Au}$ is [in $\mathrm{disintegration} {\mathrm{second}}^{-1}$]:

At time $t=0$, a material is composed of two radioactive atoms $A$ and $B$, where $N_A\left(0\right)=2N_B\left(0\right)$. The decay constant of both kind of radioactive atoms is $\lambda$. However, $A$ disintegrates to $B$ and $B$ disintegrates to $C$. Which of the following figures represents the evolution of $\frac{N_B\left(t\right)}{N_B\left(0\right)}$ with respect to time $t$?

$M_n$ and $M_p$ represent the mass of neutron and proton, respectively. An element having mass $M$ and $N$ neutron, $Z$-protons, then the correct relation will be

In the nucleus of an atom, neutrons are in excess, then emitted particles are

After a time equal to four half lives, the amount of radioactive material remaining undecayed is -

The main source of energy of the sun is

Enormous energy generation in the sun and the stars is due to