For a substance the average life for alpha - | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\lambda_{\alpha}=\frac{1}{1620}$ per year and $\lambda_{\beta}=\frac{1}{405}$ per year and it is given that the fraction of the remained activity $\f

Vedclass · Accepted Answer

$449$

Vedclass · Answer

$\lambda_{\alpha}=\frac{1}{1620}$ per year and $\lambda_{\beta}=\frac{1}{405}$ per year and it is given that the fraction of the remained activity $\frac{\mathrm{A}}{\mathrm{A}_{0}}=\frac{1}{4}$

Total decay constant

$\lambda=\lambda_{\alpha}+\lambda_{\beta}=\frac{1}{1620}+\frac{1}{405}=\frac{1}{324}$ per year

We know that $\mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-\lambda t} \Rightarrow \mathrm{t}=\frac{1}{\lambda} \log _{\mathrm{e}} \frac{\mathrm{A}_{0}}{\mathrm{A}}$

$ \Rightarrow \mathrm{t} =\frac{1}{\lambda} \log _{\mathrm{e}} 4=\frac{2}{\lambda} \log _{\mathrm{e}} 2 $

$=324 	imes 2 	imes 0.693=449 \mathrm{\,years} $

For a substance the average life for $\alpha $ -emission is $1620\ years$ and for $\beta $ emission is $405\ years$ . After how much time the $\frac {1}{4}$ of the material remains by simultaneous emission ............ $years$

Similar Questions

The half-life of a radioactive substance is $48$ hours. How much time will it take to disintegrate to its $\frac{1}{{16}} \,th$ part ............$hour$

State the relation between average life and decay constant.

A radioactive decay chain starts from $_{93}N{p^{237}}$ and produces $_{90}T{h^{229}}$ by successive emissions. The emitted particles can be

A sample contains $16\, gm$ of a radioactive material, the half life of which is two days. After $32\, days,$ the amount of radioactive material left in the sample is