Radioactive material $'A'$ has decay constant $8 \lambda$ and material $'B'$ has decay constant $ ' \lambda '$. Initially they have same number of nuclei . After what time, the ratio of number of nuclei of material $'B'$ to that $'A'$ will be $\frac{1}{e}$ ?

Assertion : If the half life of a radioactive substance is $40\, days$ then $25\%$ substance decay in $20\, days$

Reason : $N = {N_0}\,{\left( {\frac{1}{2}} \right)^n}$

where, $n = \frac{{{\rm{time\, elapsed}}}}{{{\rm{half \,life \,period}}}}$

The half-life of a particle of mass $1.6 \times 10^{-26} \,kg$ is $6.9 \,s$ and a stream of such particles is travelling with the kinetic energy of a particle being $0.05 \,eV$. The fraction of particles which will decay, when they travel a distance of $1 \,m$ is

Define the average life of a radioactive sample and obtain its relation to decay constant and half life. 

Activities of three radioactive substances $A , B$ and $C$ are represented by the curves $A, B$ and $C,$ in the figure. Then their half-lives $T _{\frac{1}{2}}( A ): T _{\frac{1}{2}}( B ): T _{\frac{1}{2}}( C )$ are in the ratio

The rate of disintegration of fixed quantity of a radioactive element can be increased by