In a sample of radioactive material,what frac | vedclass

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

Question

(C) The law of radioactive decay is given by the formula $N = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$,where $N$ is the number of nuclei remaining,

Vedclass · Accepted Answer

$1/\sqrt{2}$

Vedclass · Answer

(C) The law of radioactive decay is given by the formula $N = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$,where $N$ is the number of nuclei remaining,$N_0$ is the initial number of nuclei,$t$ is the time elapsed,and $T_{1/2}$ is the half-life.Given that the time elapsed is half of a half-life,we have $t = \frac{1}{2} T_{1/2}$.Substituting this into the decay formula:$\frac{N}{N_0} = \left( \frac{1}{2} \right)^{(T_{1/2}/2) / T_{1/2}}$$\frac{N}{N_0} = \left( \frac{1}{2} \right)^{1/2}$$\frac{N}{N_0} = \frac{1}{\sqrt{2}}$Therefore,the fraction of nuclei remaining is $1/\sqrt{2}$.

In a sample of radioactive material,what fraction of the initial number of active nuclei will remain undisintegrated after half of a half-life of the sample?

Similar Questions

If the mass of a radioactive sample is doubled,the activity of the sample and the disintegration constant of the sample are respectively

The half-life of a particle of mass $1.6 \times 10^{-26} \,kg$ is $6.9 \,s$. $A$ stream of such particles is travelling with a kinetic energy of $0.05 \,eV$ per particle. The fraction of particles that will decay when they travel a distance of $1 \,m$ is

The plot of the number $(N)$ of undecayed atoms versus activity $(A)$ of a radioactive substance is

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5$ minutes. The time (in minutes) at which the activity reduces to half of its initial value is

$A$ radioactive sample disintegrates via two independent decay processes having half-lives $T_{1/2}^{(1)}$ and $T_{1/2}^{(2)}$ respectively. The effective half-life $T_{1/2}$ of the nuclei is

Vedclass Test Series

Exam Paper Generator

Online Exam Module