Activity of a freshly prepared radioactive sample is 10^{10} disintegrations per second, whose mean

English

Gujarati

Hindi

13.Nuclei

hard

The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^9 s$. The mass of an atom of this radioisotope is $10^{-25} kg$. The mass (in $mg$ ) of the radioactive sample is

A

$1$

B

$2$

C

$3$

D

$4$

(IIT-2011)

Solution

Given: $\frac{ dN }{ dt }=10^{10}$

Mean Life $=10^9 s$

$\frac{1}{\lambda}=10^9 s$

$\lambda=10^{-9} s^{-1}$

FIrst order decay:

$\frac{ dN }{ dt }=\lambda N$

$\lambda N =10^{10}$

$N=10^{17}$

Mass of Radioactive sample $=10^{19} \times 10^{-25} kg=10^{-6} kg$

$M =10^{-6} kg=10^{-3} gms =1 mg$

Standard 12

Physics

Share

Similar Questions

Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is

$\mathop {^{38}S}\limits_{sulpher} \xrightarrow[{ – 2.48\,h}]{{half\,year}}\mathop {^{38}Cl}\limits_{chloride} \xrightarrow[{ – 0.62\,h}]{{half\,year}}\mathop {^{38}Ar}\limits_{Argon} $

Assume that we start with $1000$ $^{38}S$ nuclei at time $t = 0$. The number of $^{38} Cl$ is of count zero at $ t=0$ an will again be zero at $t = \infty $. At what value of $t,$ would the number of counts be a maximum ?

medium

An archaeologist analyses the wood in a prehistoric structure and finds that $C^{14}$ (Half life $= 5700\, years$) to $C^{12}$ is only one-fourth of that found in the cells of buried plants. The age of the wood is about ……….$years$

easy

(AIIMS-2013)

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an

medium

(AIPMT-2009)

The half-life of radon is $3.8\, days$. Three forth of a radon sample decay in …………$days$

medium

If ${N_0}$ is the original mass of the substance of half life period ${T_{1/2}} = 5$ years, then the amount of substance left after $15$ years is

medium

(AIEEE-2002)