$A$ radioactive element has a half-life period of $800$ years. After $6400$ years,what fraction of the initial amount will remain?

If the half-life of a radioactive material is $10 \ years$,then the percentage of the material decayed in $30 \ years$ is (in $\%$)

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

The relation between $\lambda$ and $T_{1/2}$ is ($T_{1/2} = \text{half-life}$,$\lambda = \text{decay constant}$)

$A$ radioactive sample has a half-life of $3$ years. The time required for the activity of the sample to reduce to $\frac{1}{5}$th of its initial value is about (in $years$)

Half-life of a radioactive substance is $20 \, min$. The time between $20\%$ and $80\%$ decay will be ......... $min$.