The half-life of a stream of radioactive part | vedclass

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

Question

(A) Given,$K.E. = 4 	ext{ eV} = 4 	imes 1.6 	imes 10^{-19} 	ext{ J} = 6.4 	imes 10^{-19} 	ext{ J}$.Mass $m = 3.2 	imes 10^{-21} 	ext{ kg}$.Usi

Vedclass · Accepted Answer

$87.5$

Vedclass · Answer

(A) Given,$K.E. = 4 	ext{ eV} = 4 	imes 1.6 	imes 10^{-19} 	ext{ J} = 6.4 	imes 10^{-19} 	ext{ J}$.Mass $m = 3.2 	imes 10^{-21} 	ext{ kg}$.Using $K.E. = \frac{1}{2}mv^2$,we get $v = \sqrt{\frac{2 	imes K.E.}{m}} = \sqrt{\frac{2 	imes 6.4 	imes 10^{-19}}{3.2 	imes 10^{-21}}} = \sqrt{4 	imes 10^2} = 20 	ext{ m/s}$.Time taken to travel $D = 3.6 	ext{ km} = 3600 	ext{ m}$ is $t = \frac{D}{v} = \frac{3600}{20} = 180 	ext{ s} = 3 	ext{ minutes}$.Since the half-life $T_{1/2} = 1 	ext{ minute}$,the time $t = 3 	ext{ half-lives}$.The number of particles remaining is $N = N_0 \left(\frac{1}{2}ight)^n = N_0 \left(\frac{1}{2}ight)^3 = \frac{N_0}{8}$.The number of particles decayed is $N_0 - N = N_0 - \frac{N_0}{8} = \frac{7}{8}N_0$.The percentage of decayed particles is $\frac{7/8 N_0}{N_0} 	imes 100 = 87.5\%$.

Similar Questions

$A$ radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5$ minutes,the rate is $1250$ disintegrations per minute. Then,the decay constant (per minute) is (in $, \ln 2$)

$Rn$ decays into $Po$ by emitting an $\alpha$-particle with a half-life of $4 \text{ days}$. $A$ sample contains $6.4 \times 10^{10}$ atoms of $Rn$. After $12 \text{ days}$,the number of atoms of $Rn$ left in the sample will be:

$A$ radioactive nucleus can decay by two different processes. The half-life for the first process is $3.0 \, hours$ while it is $4.5 \, hours$ for the second process. The effective half-life of the nucleus will be $......... \, hours.$

Half-lives for $\alpha$ and $\beta$ emission of a radioactive material are $16$ years and $48$ years respectively. When the material decays by giving $\alpha$ and $\beta$ emission simultaneously,the time in which $3/4$th of the material decays is ....... years.

The half-life period of a radioactive element $A$ is $62 \text{ years}$. It decays into another stable element $B$. An archaeologist found a sample in which $A$ and $B$ are in $1 : 15$ ratio. The age of the sample is (in $\text{ years}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module