A box contains a radioactive material of mass 14.58 gram at time t=0. What is the mass ofo the element left in the box after a time of 2 mean lives ? (take e=2.7)

Options

A. a) 4.5g
B. b) 3.7g
C. c) 2g
D. d) 1.1g

Answer

C

Explanation

The mass is proportional to the number of radioactive nuclei. Hence we use `N= N_0e^(-lamdat)`
In this case, t=2 (mean lives) `=2tau`
and `tau = 1/lamda therefore t =2/lamda`
`therefore N = N_0 e^(2/lamdaxxlamda) = N_0e^(-2) = (N_0)/(e^2)`
`therefore N = (14.58)/((2.7)^2) (14.58)/(7.29) = 2g`
`therefore` The mass of the element left after 2 half lives = 2g