The half-life of radium is about $1600$ years. Of $100\, g$ of radium existing now, $25\, g$ will remain unchanged after .......... $years$

$37$ Rutherford equals

A radioactive element has half life period $800$ years. After $6400$ years what amount will remain?

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

$1 \,mg$ gold undergoes decay with $2.7$ days half-life period, amount left after $8.1$ days is ......... $mg$

A radio nuclide $A_1$ with decay constant $\lambda_1$  transforms into a radio nuclide $A_2$ with decay constant $\lambda_2$ . If at the initial moment the preparation contained only the radio nuclide $A_1$, then the time interval after which the activity of the radio nuclide $A_2$ reaches its maximum value is :-