In a sample of a radioactive substance, what fraction of the initial nuceli will remain undecayed after a time `t=T//2` , where T=half -life of radioactive substance?

Options

A. `(1)/(sqrt2)`
B. `(1)/(2sqrt2)`
C. `(1)/(4)`
D. `(1)/(sqrt2-1)`

Answer

a

Explanation

Fraction of nuclei which reamin undecayed is
`f=(N)/(N_(0)) =(N_0 e^(-lambda t))/(N_(0))`
=`e^(-lambda t)`
=`e^((_1n/T)(T/2))`
`=(1)/(e^(1n (sqrt2)) =(1)/(sqrt2)`