Question

The half-life of a radioactive sample undergoing ${\displaystyle \alpha }$ - decay is 1.4 x 10¹⁷ s. If the number of nuclei in the sample is 2.0 x 10²¹, the activity of the sample is nearly ____________.

विकल्प

• 10³ Bq

• 10⁴ Bq

• 10⁵ Bq

• 10⁶ Bq

Answer 1

The half-life of a radioactive sample undergoing ${\displaystyle \alpha }$ - decay is 1.4 x 10¹⁷ s. If the number of nuclei in the sample is 2.0 x 10²¹, the activity of the sample is nearly 10⁴ Bq.

Explanation:

Activity of the sample is given by,

${\displaystyle \left|\text{R}\right|=\lambda \text{N}}$

${\displaystyle \left|\text{R}\right|=\frac{0.693}{\text{T}}\times \text{N}}$

${\displaystyle \left|\text{R}\right|=\frac{0.693}{1.4\times {10}^{17}}\times 2\times {10}^{21}}$

${\displaystyle \left|\text{R}\right|=9900\approx 10000}$

${\displaystyle ={10}^4 \text{Bq}}$