In a radioactive disintegration,the ratio of the initial number of atoms to the number of atoms present at time $t = \frac{1}{2 \lambda}$ is $[\lambda = \text{decay constant}]$

$A$ radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5\, minutes$,the rate becomes $1250$ disintegrations per minute. Then,its decay constant (per minute) is

The half-life $(T)$ and the disintegration constant $(\lambda)$ of a radioactive substance are related as:

Two radioactive substances $A$ and $B$ have the same number of initial nuclei. If the half-lives of $A$ and $B$ are $1.5 \ days$ and $4.5 \ days$ respectively, then the ratio of the number of nuclei remaining in $A$ and $B$ after $9 \ days$ is

In a nuclear reactor,the activity of a radioactive substance is $2000 / s$. If the mean life of the products is $50 \text{ minutes}$,then in the steady power generation,the number of radionuclides is:

$A$ radioactive substance has decay constants $\lambda_{\alpha}$ and $\lambda_{\beta}$ for $\alpha$ and $\beta$ emission,respectively. If the substance emits both $\alpha$ and $\beta$ particles,find the effective half-life of the substance.