Question

The counting rate observed from a radioactive source at t = 0 second was 1600 counts per second and at t = 8 seconds it was 100 counts per second. The counting rate observed as counts per second at t = 6 seconds will be

• A. 400
• B. 300
• C. 200
• D. 150

Answer 1

The correct option is C 200

By using $A=A_0{\left(\frac{1}{2}\right)}^n\Rightarrow 100=1600{\left(\frac{1}{2}\right)}^{\frac{8}{T_{1/2}}}\Rightarrow \frac{1}{16}={\left(\frac{1}{2}\right)}^{\frac{8}{T_{1/2}}}\Rightarrow T_{1/2}=2sec$
Again by using the same relation the count rate at t = 6 sec will be $A=1600{\left(\frac{1}{2}\right)}^{\frac{6}{2}}=200$.