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

If $f$ denotes the ratio of the number of nuclei decayed $(N_{d})$ to the number of nuclei at $t=0$ $(N_{0})$,then for a collection of radioactive nuclei,the rate of change of $f$ with respect to time is given as: [$\lambda$ is the radioactive decay constant]

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?

State the law of radioactive decay.

The half-life of radium is $1600 \, \text{years}$. The fraction of the radium sample that will remain after $6400 \, \text{years}$ is:

The half-life of a radioactive nucleus is $50$ days. The time interval $(t_2 - t_1)$ between the time $t_2$ when $2/3$ of it has decayed and the time $t_1$ when $1/3$ of it has decayed is ...... days.

Vedclass Test Series

Exam Paper Generator

Online Exam Module