At `t=0`, number of radioactive nuclei of a radioactive substance are x and its radioactivity is y. Half-life of radioactive substance is T. Then,

Options

A. (a) `x/y` is constant throughout
B. (b) `x/ygtT`
C. (c) value of `xy` remains half after one half-life
D. (d) value of `xy` remains one fourth after one half-life

Answer

A, B, D

Explanation

`y=lambdax=(1n2)/(T).x`
`x/y=1/lambda=constant`
`x/y=(T)/(1n2)` or `x/ygtT` (as `1n2=0.693)`
Further,
`xy=x(lambdax)=lambdax^2`
After one half-life, x remains half. Hence, `x^2` remains `1/4th`.