Two radioactive substances A and B have decay constants 5 and res… - Vidyadip

MCQ

Two radioactive substances $A$ and $B$ have decay constants $5\lambda $ and $\lambda $ respectively. At $t = 0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $(\frac {1}{e})^2$ will be

A
$1/\lambda $
B
$1/4\lambda $
C
$2/\lambda $
✓
$1/2\lambda $

✓

Answer

Correct option: D.

$1/2\lambda $

d
$\frac{1}{{{e^2}}} = {e^{\lambda t - 5\lambda t}}$

$t\, = \,\frac{1}{{2\lambda }}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 13. Nuclei→13. Nuclei — all question types→Physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Two long current carrying thin wires, both with current $I$, are held by insulating threads oflength $L$ and are in equilibrium as shown in the figure, with threads making an angle '$\theta$' with the vertical. If wires have mass $\lambda$ per unit length then the value of $l$ is
($g =$ gravitational acceleration)

In the given figure force on wire $ABC$ will be $(B = 2T)$

If $X, Y$ and $Z$ in figure are identical lamps, which of the following changes to the brightnesses of the lamps occur when switch $S$ is closed?

The radius of curvature of convex surface of a thin plano-convex lens is $15 cm$ and refractive index of its material is $1.6.$ The power of the lens will be

Given below are three schematic graphs of potential energy $V(r)$ versus distance $r$ for three atomic particles : electron $\left(e^{-}\right)$, proton $\left(p^{+}\right)$and neutron $(n)$, in the presence of a nucleus at the origin $O$. The radius of the nucleus is $r_0$. The scale on the $V$-axis may not be the same for all figures. The correct pairing of each graph with the corresponding atomic particle is

Three capacitors each of capacitance $1\,\mu F$ are connected in parallel. To this combination, a fourth capacitor of capacitance $1\,\mu F$ is connected in series. The resultant capacitance of the system is.......$\mu F$

A 100 W bulb $B_1$, and two $60-\mathrm{W}$ bulbs $B_2$ and $B_3$, are connected to a 250 V source, as shown in the figure. Now $W_1$, $W_2$ and $W_3$ are the output powers of the bulbs $B_1, B_2$ and $B_3$, respectively. Then

The current I in an induction coil varies with time t according to the graph shown in the figure. Which of the following graphs shows the induced emf (ε)in the coil with time.

The minimum frequency $\nu $ of continuous $X-$ rays is related to the applied potential difference $V$ as

The total intensity of earth's magnetic field at the magnetic equator is $5$ $units$. Its value at a magnetic latitude of $37^o $ is equal to