Question

A radioactive material has a halflife of $8$ hours and causes a counter to register $180$ counts/min. Find out the count rate for this sample two days later ?

• A. $1.4/min$
• B. $2.8/min$
• C. $5.6/min$
• D. $11.2/min$
• E. $22.4/min$

Answer 1

Answer: (B)

$2.8/min$

If $T$ is the half life of radioactive substance then,

$\frac{R}{R_0}={\left(\frac{1}{2}\right)}^{\frac{t}{T}}$

Given: $T=8hr,t=2days=48hr,R_0=180counts/min,R=?$

Therefore,

$\frac{R}{R_0}={\left(\frac{1}{2}\right)}^{\frac{48}{8}}$

$\frac{R}{R_0}={\left(\frac{1}{2}\right)}^6$

$R=R_0\times 1/64=180/64=2.8/min$