There are 10^{10} radioactive nuclei in a given radioactive element, Its half-life time is 1, minute

English

Gujarati

Hindi

13.Nuclei

medium

There are $10^{10}$ radioactive nuclei in a given radioactive element, Its half-life time is $1\, minute.$ How many nuclei will remain after $30\, seconds?$

$(\sqrt{2}=1.414)$

A

$2 \times 10^{10}$

B

$7 \times 10^{9}$

C

$10^{5}$

D

$4 \times 10^{10}$

(JEE MAIN-2021)

Solution

$\frac{{N}}{{N}_{0}}=\left(\frac{1}{2}\right)^{\frac{{t}}{t_{\frac{1}{2}}}}$

$\frac{{N}}{10^{10}}=\left(\frac{1}{2}\right)^{\frac{30}{60}}$

${N}=10^{10} \times\left(\frac{1}{2}\right)^{\frac{1}{2}}=\frac{10^{10}}{\sqrt{2}} \approx 7 \times 10^{9}$

Standard 12

Physics

Share

Similar Questions

Why radioactivity is considered a nuclear phenomenon ?

easy

In a radioactive decay chain reaction, ${ }_{90}^{230} Th$ nucleus decays into ${ }_{84}^{214} Po$ nucleus. The ratio of the number of $\alpha$ to number of $\beta^{-}$particles emitted in this process is. . . . .

hard

(IIT-2022)

Two radioactive elements $R$ and $S$ disintegrate as
$R \rightarrow P + \alpha; \lambda_R = 4.5 × 10^{-3} \,\, years^{-1}$
$S \rightarrow P + \beta; \lambda_S = 3 × 10^{-3} \,\, years^{-1}$
Starting with number of atoms of $R$ and $S$ in the ratio of $2 : 1,$ this ratio after the lapse of three half lives of $R$ will be :

normal

Radioactivity was discovered by

easy

A radioactive sample decays by $\beta$ -emission. In first two seconds $‘n’$ $\beta$ -particles are emitted and in next $2\ seconds$ , $‘0.25n’$ $\beta$ -particles are emitted. The half life of radioactive nuclei is …… $sec$

medium