The half-life of a radioactive substance is 2 | 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 $N(t) = N_0 e^{-\lambda t}$.At time $t_1$,the amount decayed is $\frac{1}{3} N_0$,so the remaining amount is

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(C) The radioactive decay law is given by $N(t) = N_0 e^{-\lambda t}$.At time $t_1$,the amount decayed is $\frac{1}{3} N_0$,so the remaining amount is $N_1 = N_0 - \frac{1}{3} N_0 = \frac{2}{3} N_0$.At time $t_2$,the amount decayed is $\frac{2}{3} N_0$,so the remaining amount is $N_2 = N_0 - \frac{2}{3} N_0 = \frac{1}{3} N_0$.We observe that $N_2 = \frac{1}{2} N_1$.Since the amount of substance reduces to half of its value in one half-life period $(T_{1/2})$,the time interval required for the substance to decay from $N_1$ to $N_2$ is exactly one half-life.Therefore,$t_2 - t_1 = T_{1/2} = 20 \, min$.

The half-life of a radioactive substance is $20 \, min$. The approximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and the time $t_1$ when $\frac{1}{3}$ of it has decayed is ......... $min$.

Similar Questions

If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ in four points $(x_i, y_i)$,for $i=1, 2, 3, 4$,then $y_1+y_2+y_3+y_4$ equals

The collector plate in an experiment on the photoelectric effect is kept vertically above the emitter plate. $A$ light source is turned on and a saturation photocurrent is recorded. An electric field is then switched on which has a vertically downward direction.

$3$ moles of ethanol react with $1$ mole of phosphorus tribromide to form $3$ moles of bromoethane and $1$ mole of $X$. Which of the following is $X$?

If $3x^2-11xy+10y^2-7x+13y+k=0$ denotes a pair of straight lines,then the point of intersection of the lines is

The magnitude of the projection of the vector $\vec{a} = 4\hat{i} - 3\hat{j} + 2\hat{k}$ on the line which makes equal angles with the coordinate axes is

Vedclass Test Series

Exam Paper Generator

Online Exam Module