Question

A radioactive substance is being produced at a constant rate of 200 nuclei/s. The decay constant of the substance is 1 s^–1. After what time the number of radioactive nuclei will become 100. Initially there are no nuclei present?

• A. 1 s
• B. $rac{1}{\ln(2)}$s
• C. ln (2) s
• D. 2 s

Answer 1

Answer: (C)

ln (2) s

Answer 2

Let N be the number of nuclei at any time t. Then

$\frac { \mathrm { dN } } { \mathrm { dt } }$ = 200 – l N

\ =

or N =$\frac { 200 } { \lambda }$ (1 – e^–lt)

Given that N = 100 and l = 1 s^–1

\ 100 = 200 (1 – e^–t)

or e^–t = $\left( \frac { 1 } { 2 } \right)$

\ t = ln (2) sec