Question 410: Atoms & Nuclei

Question

A radioactive element having half-life 30 min . is undergoing beta decay. The fraction of radioactive element remains undecayed after 90 min . will be

Accepted Answer

We use the formula:
$$  \frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^{\frac{t}{T}}  $$
Here,

$ t = 90 $ min (total time passed), and

$ T = 30 $ min (half-life).
So,

$ \frac{t}{T} = \frac{90}{30} = 3 $
Substitute this in the formula:

$$ \frac{\mathrm{N}}{\mathrm{N}_0} = \left(\frac{1}{2}\right)^3 = \frac{1}{8} $$
This means after 90 minutes,

$\frac{1}{8}$ of the radioactive element is still left, or not decayed.

Answer

$\frac{1}{2}$

Answer

$\frac{1}{4}$

Answer

$\frac{1}{8}$

Answer

$\frac{1}{16}$

Atoms & Nuclei

A radioactive element having half-life 30 min . is undergoing beta decay. The fraction of radioactive element remains undecayed after 90 min . will be

Choose the correct answer: