2002 AIPMT NucleiRadioactive Decay and Half-life Easy Question 4 of 5 in Radioactive Decay and Half-life

A sample of radioactive element containing $4 \times 10^{16}$ active nuclei. Half life of element is 10 days, then number of decayed nuclei after 30 days : -

A $0.5 \times 10^{16}$
B $2 \times 10^{16}$
C $3.5 \times 10^{16}$
D $1 \times 10^{16}$

The answer is C.

Solution

Number of half lives: $n = \dfrac{t}{T_{1/2}} = \dfrac{30}{10} = 3$
Active nuclei left: $X = \dfrac{X_0}{2^n} = \dfrac{4 \times 10^{16}}{2^3} = 0.5 \times 10^{16}$
Decayed nuclei $= X_0 - X = 4 \times 10^{16} - 0.5 \times 10^{16}$
$= 3.5 \times 10^{16}$

Concept Decayed nuclei after n half lives

Radioactive Decay and Half-life in past papers

5 questions from this chapter have appeared across 5 exam years.