MCQ
A radioactive element emits $200$ particles per second. After three hours $25$ particles per second are emitted. The half life period of element will be ..........$minntes$
- A$50$
- ✓$60 $
- C$70$
- D$80$
✓
Answer
Correct option: B.
$60 $
b
(b) $R = \frac{{dN}}{{dt}} \propto N$
(b) $R = \frac{{dN}}{{dt}} \propto N$
$\Rightarrow \frac{{{R_2}}}{{{R_1}}} = \frac{{{N_2}}}{{{N_1}}}$
But $\frac{{{N_2}}}{{{N_1}}} = {\left( {\frac{1}{2}} \right)^{{t_{1/2}}}}$
$\Rightarrow \frac{{25}}{{200}} = \frac{1}{8} = {\left( {\frac{1}{2}} \right)^3}$
$\Rightarrow \frac{t}{{{t_{1/2}}}} = 3$
$\therefore {t_{1/2}} = \frac{t}{3} = \frac{3}{3} = 1\;hour = 60\,minutes$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A transverse wave is passing through a string shown in figure. Mass density of the string is $1 \ kg/m^3$ and cross section area of string is $0.01\ m^2.$ Equation of wave in string is $y = 2sin (20t - 10x).$ The hanging mass is (in $kg$):-
→If speed of a particle moving in a circle of radius $2\,m$ is given as $v = 2t + 2$, then its centripetal acceleration after $1\, s$ will be ......... $m/s^2$
→A particle is performing $S.H.M.$ with energy of vibration $90 \,J$ and amplitude $6 \,cm$. When the particle reaches at distance $4 \,cm$ from mean position, it is stopped for a moment and then released. The new energy of vibration will be ........... $J$
→A boy of height $1.5\,m$ with his eye level at $1.4\, m$ stands before a plane mirror of length $0.75$ fixed on the wall. The height of the lower edge of the mirror above the floor is $0.8\,m$, then
→Given below are two statements:
→Statement $I$ : The diamagnetic property depends on temperature.
Statement $II$ : The included magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field.
In the light of given statement, choose the correct answer from the options given below:
If two streams of protons move parallel to each other in the same direction, then they
The circuit diagram shown here corresponds to the logic gate,
Which is different from others by units
The value of the acceleration due to gravity is $g _{1}$ at a height $h =\frac{ R }{2}( R =$ radius of the earth) from the surface of the earth. It is again equal to $g _{1}$ at a depth $d$ below the surface of the earth. The ratio $\left(\frac{ d }{ R }\right)$ equals
→When a charged particle enters a uniform magnetic field its kinetic energy