A 16, g sample of a radioactive element is ta | vedclass

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

Question

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

Vedclass · Accepted Answer

$\frac{1}{2}\, hour$

Vedclass · Answer

(C) The radioactive decay law is given by $N = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$,where $N$ is the remaining amount,$N_0$ is the initial amount,$t$ is the time elapsed,and $T_{1/2}$ is the half-life.Given: $N_0 = 16\, g$,$N = 1\, g$,and $t = 2\, hours$.Substituting these values into the formula:$1 = 16 \left( \frac{1}{2} \right)^{2/T_{1/2}}$$\frac{1}{16} = \left( \frac{1}{2} \right)^{2/T_{1/2}}$$\left( \frac{1}{2} \right)^4 = \left( \frac{1}{2} \right)^{2/T_{1/2}}$Equating the exponents:$4 = \frac{2}{T_{1/2}}$$T_{1/2} = \frac{2}{4} = \frac{1}{2}\, hour$.

$A$ $16\, g$ sample of a radioactive element is taken from Bombay to Delhi in $2\, hours$ and it is found that $1\, g$ of the element remains (undisintegrated). The half-life of the element is:

Similar Questions

Consider a radioactive material of half-life $1.0 \, \text{minute}$. If one of the nuclei decays now,the next one will decay

The curve between the activity $A$ of a radioactive sample and the number of active atoms $N$ is

The relation between the mean life time $\tau$ and the half-life time $T_{1/2}$ of a radioactive substance is:

The activity of a radioactive sample:

In an old rock,the ratio of uranium to lead nuclei is $1:1$. The half-life of uranium is $4.5 \times 10^9$ years. If the rock initially contained only uranium nuclei,how old is the rock?

Vedclass Test Series

Exam Paper Generator

Online Exam Module