Question

In a given radio-active sample, there are ${10}^{24}$ nuclei present. If its half life period is 20 years, how many nuclei will be present after 10 years ? (Take $1/\sqrt{2}=0.707$)

• A. $4.07\times {10}^{23}$
• B. $6.07\times {10}^{23}$
• C. $7.07\times {10}^{23}$
• D. $14.14\times {10}^{23}$

Answer 1

The correct option is C $7.07\times {10}^{23}$

The number of nuclei (N) present after ${}^{\prime }{n}^{\prime }$ half lives is given by
$N=N_0{\left(\frac{1}{2}\right)}^n\to$ where $n=\frac{t}{T}$
In the question, we are given that $N_0={10}^{24}$; $n=10/20=1/2$; $N=$ ?
Substituting the above values in equation (1), we get
$N={10}^{24}{\left(\frac{1}{2}\right)}^{\frac{1}{2}}={10}^{24}\times 0.707=7.07\times {10}^{23}$