MCQ
A radioactive material decays by simultaneous emission of two particles with respective half lives $1620$ and $810$ years. The time (in years) after which one- fourth of the material remains is
- ✓$1080$
- B$2430$
- C$3240$
- D$4860$
✓
Answer
Correct option: A.
$1080$
a
(a) $\lambda = {\lambda _1} + {\lambda _2} \Rightarrow \frac{1}{T} = \frac{1}{{{T_1}}} + \frac{1}{{{T_2}}}$
(a) $\lambda = {\lambda _1} + {\lambda _2} \Rightarrow \frac{1}{T} = \frac{1}{{{T_1}}} + \frac{1}{{{T_2}}}$
$\therefore T = \frac{{{T_1}{T_2}}}{{{T_1} + {T_2}}} = \frac{{810 \times 1620}}{{810 + 1620}} = 540\;years$
Hence $\frac{1}{4} \,th$ of material remain after $1080$ years.
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
Two particles $X$ and $Y$ having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The ratio of the mass of $X$ to that of $Y$ is:
→The electric potential decreases uniformly from $120V$ to $80V$ as one moves on the x-axis from $x = -1cm$ to $x = + 1cm.$ The electric field at the origin.
→The width of the $nth$ $HPZ$ will be
→A piece of wood from a recently cut tree shows $20\,decays$ per minute. A wooden piece of same size placed in a museum ( obtained from a tree cut many years back) shows $2\,decays$ per minute. If half life of $C^{14}$ is $5730\, years$, then age of the wooden piece placed in the museum is approximately ........... $years$
→The radioactivity of a certain radioactive element drops to 1/64 of its initial value in 30 seconds. Its half life is
An observer can see through a small hole on the side of a jar (radius $15\, cm$ ) at a point at height of $15\, cm$ from the bottom (see figure). The hole is at a height of $45\, cm$. When the jar is filled with a liquid up to a height of $30\, cm$ the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid $N / 100,$ where $N$ is an integer, the value of $N$ is $.....$
→A radioactive sample of $U^{238}$ decay to $Pb$ through a process for which half life is $4.5 \times 10^9$ years. The ratio of number of nuclei of Pb to $\mathrm{U}^{238}$ after a time of $1.5 \times 10^9$ years $($given $2^{1 / 3}=1.26 )$
→Which of the energy band diagrams shown in the figure corresponds to that of a semiconductor
A magnetic field cannot exert any force on a:
A parallel plate capacitor with air between the plates has a capacitance of $9\,pF$. The separation between its plates is $'d'$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1=3$ and thickness $\frac {d}{3}$ while the other one has dielectric constant $K_2 = 6$ and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now........$pF$
→