The half-life period of a radioactive substance is 5 { min}. The amount of substance decayed in 20 { min} will be

Correct Answer is : 93.75%93.75\%93.75%

Correct Answer is : 93.75%93.75\%93.75%

Test Index

CGPET 2021 Solved Paper

Section: Physics

Question : 6 of 150

Marks: +1, -0

5 \text{ min}

20 \text{ min}

Solution:

Given, half - life period of a radioactive substance,

T_{1/2} = 5 \text{ min}

Total time,

T = 20 \text{ min}

Number of half - life,

n = \frac{\text{Total time }(T)}{\text{Half-life }(T_{1/2})} = \frac{20}{5} = 4

After n half - life, the amount of substance undecayed,

N = N_0 \left(\frac{1}{2}\right)^n

Fraction undecayed

= \frac{N}{N_0} = \left(\frac{1}{2}\right)^4

∴ Fraction decayed

= 1 - \frac{N}{N_0}

= 1 - \left(\frac{1}{2}\right)^4 = \frac{15}{16}

Therefore, percentage decayed amount

= \left(\frac{15}{16} \times 100\right)\% = 93.75\%

Go to Question:

Prev Question

Next Question