Question
A radioactive nucleus decays by two different processes. The half life for the first process is $10\, s$ and that for the second is $100 s$. the effective half life of the nucleus is close to$.....sec$
✓
Answer
a
$\frac{1}{ T _{\text {eff }}}=\frac{1}{ T _{1}}+\frac{1}{ T _{2}}$
$\frac{1}{ T _{\text {eff }}}=\frac{1}{ T _{1}}+\frac{1}{ T _{2}}$
$T _{ eff }=\frac{ T _{1} T _{2}}{ T _{1}+ T _{2}}=\frac{1000}{110}=\frac{100}{11}=9.09$
$T _{ eff } \cong 9$
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
The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar shown in the figure. What will be the temperature at the junction of copper and steel ....... $^oC$
→$0.2\, F$ capacitor is charged to $600\, V$ by a battery. On removing the battery. It is connected with another parallel plate condenser of $1\, F$. The potential decreases to....$V$
→A particle $(\mathrm{m}=1\; \mathrm{kg})$ slides down a frictionless track $(AOC)$ starting from rest at a point $A$ (height $2\; \mathrm{m}$ ). After reaching $\mathrm{C}$, the particle continues to move freely in air as a projectile. When it reaching its highest point $P$ (height $1 \;\mathrm{m}$ ). the kinetic energy of the particle (in $\mathrm{J}$ ) is : (Figure drawn is schematic and not to scale; take $\left.g=10 \;\mathrm{ms}^{-2}\right)$
→A large tank is filled with water to a height $H$. A small hole is made at the base of the tank. It takes ${T_1}$ time to decrease the height of water to $\frac{H}{\eta }\,(\eta > 1)$; and it takes ${T_2}$ time to take out the rest of water. If ${T_1} = {T_2}$, then the value of $\eta $ is
→The current through an ideal $PN-$junction shown in the following circuit diagram will be .....$mA$
→In a lossless transformer an alternating current of $2\, amp$ is flowing in the primary coil. The number of turns in the primary and secondary coils are $100$ and $20$ respectively. The value of the current in the secondary coil is.......$A$
→In the transistor circuit shown, assume that the voltage drop between the base and the emitter is $0.5\ V$ . What will be the ratio of the voltage across resistances $R_2$ & $R_1$ in order to make this circuit function as a source of constant current, $I$ = $1\ mA$ ?
→A projectile crosses two walls of equal height $H$ symmetrically as shown The height of each wall is ........ $m$
→A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{\mathrm{x}}{100}$ where x is $\qquad$
→As shown in figure, on bringing a charge $Q$ from point $A$ to $B$ and from $B$ to $C$, the work done are $2\, joule$ and $-3\, joule$ respectively. The work done to bring the charge from $C$ to $A$ is
→