Question

A sample of radioactive element contains 8 × 10¹⁶ active nuclei. The half-life of the element is 15 days. The number of nuclei decayed after 60 days is ______.

विकल्प

• 2 × 10¹⁶

• 7.5 × 10¹⁶

• 4 × 10¹⁶

• 0.5 × 10¹⁶

Answer 1

A sample of radioactive element contains 8 × 10¹⁶ active nuclei. The half-life of the element is 15 days. The number of nuclei decayed after 60 days is 7.5 × 10¹⁶.

Explanation:

Half life T = 15 days

∴ 60 days= 4 × 15 = 4 half lives

`"N"/"N"_0=(1/2)^4=1/16`

`"N"="N"_0/16=(8xx10^16)/16=0.5xx10^16`

This is the number of nuclei remaining

∴ Number of nuclei decayed

= 8 × 10¹⁶ - 0.5 × 10¹⁶

= 7.5 × 10¹⁶