Question

The half-life period of radioactive element is $140$ days. After $560$ days, $1$ gram of element will reduce to

• A. $\frac{1}{2}g$
• B. $\frac{1}{4}g$
• C. $\frac{1}{8}g$
• D. $\frac{1}{16}g$

Answer 1

Answer: (D)

$\frac{1}{16}g$

Answer 2

$T=n \times t_{1 / 2}$
Where, $t_{1 / 2}=$ half-life period,
$n=\frac{T}{t_{1 / 2}}=\frac{560}{140}=4$
Now, $N_{t}=N_{0}\left(\frac{1}{2}\right)^{n}$
$=1 \times\left(\frac{1}{2}\right)^{4}$
$=\frac{1}{16} g$