Nuclear Physics Question 4

Question 4 - 29 January - Shift 1

If a radioactive element having half-life of $30 min$ is undergoing beta decay, the fraction of radioactive element remains undecayed after $90 min$. will be :

(1) $\frac{1}{8}$

(2) $\frac{1}{16}$

(3) $\frac{1}{4}$

(4) $\frac{1}{2}$

Show Answer

Answer: (1)

Solution:

Formula: Radioactive Decay

$ \begin{aligned} & \frac{N}{N_0}=(\frac{1}{2})^{t / \frac{1}{2}}=(\frac{1}{2})^{\frac{90}{30}} \\ & \frac{N}{N_0}=(\frac{1}{2})^{3}=\frac{1}{8} \end{aligned} $