Solveeit Logo

Question

Question: A radioactive material has an initial amount 16 gm. After 120 days it reduces to 1 gm, then the half...

A radioactive material has an initial amount 16 gm. After 120 days it reduces to 1 gm, then the half-life of radioactive material is.

A

60 days

B

30 days

C

40 days

D

240 days

Answer

30 days

Explanation

Solution

NN0=(12)n(116)=(12)nn=4\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{n} \Rightarrow \left( \frac{1}{16} \right) = \left( \frac{1}{2} \right)^{n} \Rightarrow n = 4

also n=tT1/2T1/2=1204=306mudaysn = \frac{t}{T_{1/2}} \Rightarrow T_{1/2} = \frac{120}{4} = 30\mspace{6mu} days