Question

A radioactive substance has a half-life of $2$ weeks. At the beginning of an investigation, a sample
of the substance emits $3000\beta -particles$ per minute.
How many $\beta -particles$ will it emit per minute after $6$ weeks?

• A. $0$
• B. $375$
• C. $500$
• D. $1500$

Answer 1

The correct option is B $375$

Half life is $2$ weeks , and given time is $6$ weeks.

So, number of half life's spent $=\frac{6}{2}=3$ weeks

Number of particles emitted with time is given by $N=N_o\exp -\lambda t$, and after each half life the number of particles emitted will become half.

So the number of particles emitted after $6$ weeks are$=\frac{N_o}{2^3}=\frac{3000}{8}=375$