Question

Two radioactive elements $X$ and $Y$ have half lives of $50$ and $100$ minutes respectively. Initial sample of both the elements have same no. of atoms. The ratio of the remaining number of atoms of $X$ and $Y$ after $200$ minutes is

• A. $2$
• B. $\frac{1}{4}$
• C. $4$
• D. $\frac{5}{4}$

Answer 1

The correct option is B $\frac{1}{4}$

The initial sample of X and Y elements have same no of atoms.

$t_{x0.5}=50$ minutes

$t_{y0.5}=100$ minutes

$N_t=N_0{2}^{\frac{-t}{t_{0.5}}}$

after 200 minutes, remaining no of atoms of X and Y:

$\frac{N_{xt}}{N_{yt}}=\frac{2^{\frac{-200}{50}}}{2^{\frac{-200}{100}}}$

$\frac{N_{xt}}{N_{yt}}=\frac{2^{-4}}{2^{-2}}$

$\frac{N_{xt}}{N_{yt}}=2^{-2}$

$\frac{N_{xt}}{N_{yt}}=\frac{1}{4}$