Embibe Experts Solutions for Exercise 2: EXERCISE 13.2

Half life of a radioactive element is $40$ minute. What amount will remain undecayed after $4$ hour?

A radioactive substance decays by two different processes having half lives ${\mathrm{t}}_1$ and ${\mathrm{t}}_2$ respectively. When both decays take place simultaneously, the effective half life of substance is

A freshly prepared radioactive source (half life $=4$ hrs) emits radiations of intensity which is $32$ times the permissible level. The minimum time (in hr) after which it would be safe to work with this source is

Consider the following decay :
${}^{220}X\to {}^{216}Y+\mathrm{\alpha }+5.5 \mathrm{MeV}$
Kinetic energy of $\alpha$ particle is

A radioactive substance decays to $1/{16}^{\mathrm{th}}$ of its initial activity in $40$ days. The half-life of the radioactive substance expressed in days is :-

When an ${\mathrm{U}}^{238}$ nucleus originally at rest, decays by emitting an alpha particle having speed $u$, the recoil speed of the residual nucleus is

In the nuclear fusion reaction  ${}_1{}^2\mathrm{H}+{}_1{}^3\mathrm{H}\stackrel{}{\to }{}_2{}^4\mathrm{He}+\mathrm{n}$. It is given that the repulsive potential energy between the two nuclei is $~7.7\times {10}^{-14} \mathrm{J}$, the temperature at which the gases must be heated to initiate the reaction is nearly $[$Boltzmann's constant $\left.\mathrm{k}=1.38\times {10}^{-23} \mathrm{J} {\mathrm{K}}^{-1}\right]$

The activity of a radioactive sample is $1.6 \mathrm{curie}$ and its half-life is $2.5$ days. Its activity after $10$ days will be,