Question

Two radioactive samples consist of equal number of atoms.The half lives are 2 hours and 4 hours respectively.The ratio of their activities then is

Answer 1

Correct option is B. 1:2

let the $$N$$ no. of atoms in $$x$$ and $$y$$ both.

assume $$\Delta N$$ ho. af atoms decay in \Deltat time.

We knouthe rate of disintegration

$$\frac{\Delta N}{D t} \propto N$$

$$\frac{\Delta N}{\Delta t}=\lambda N$$

we know $$\lambda=\frac{0.693}{t / 2}$$

So $$\lambda_{1}=\frac{0.693}{2}, \lambda_{2}=\frac{0.693}{4}$$

$$\frac{y}{x}=\frac{\lambda N}{\lambda_{x} N}$$

$$\frac{y}{x}=\frac{0.693 \times 2}{4 \times 0.693}$$

$$\frac{y}{x}=\frac{1}{2}$$

$$[B] 1: 2$$