The half life of a particle of mass `1.6xx10^(-26) kg is 6.9` s and a stream of such particles is travelling with the kinetic energy of a particle being 0.05 eV. The fraction of particles which will decay when they travel a distance of 1 m is -

Options

A. `0.1`
B. `0.01`
C. `0.001`
D. `0.0001`

Answer

D

Explanation

`KE= (1)/(2) mv^(2)`
`rArr 0.05 xx 16 xx 10^(-19) = (1)/(2) xx 1.6 xx 10^(-26) xx v^(2)`
`rArr v= 1000` m/sec
Time taken to travel a distance 1m
`t= (1)/(1000)= 0.001` sec
Half life of radioactive material = 9.6 sec
`T_(1//2)= (0.693)/(lamda) rArr lamda = (0.693)/(6.9)= 0.1`
Fraction of particle decay in .0 001sec .
`rArr 1- e^(-lamda t)= 1- e^(0.1 xx (1)/(1000))= 0.0001`