Radioactive Decay Analysis: P → Q → R
The problem describes a sequential decay chain where radioactive material P decays into another radioactive material Q, which subsequently decays into a stable material R. We need to identify the correct representation of the time-dependent mass of P, Q, and R.
Mass Behavior of P (Parent Nucleus)
Material P is the initial radioactive substance. Its mass decreases over time due to radioactive decay. This decay follows an exponential pattern. Assuming the initial mass of P is $M_0$ at time $t=0$, its mass at time $t$, denoted as $M_P(t)$, can be described by the equation:
$M_P(t) = M_0 e^{-\lambda_1 t}$
Where $\lambda_1$ is the decay constant for P. The graph for P should start at $M_0$ and decrease asymptotically towards zero.
Mass Behavior of Q (Intermediate Nucleus)
Material Q is formed as P decays, so its mass starts increasing from zero. However, Q is also radioactive and decays into R. Therefore, the mass of Q, $M_Q(t)$, increases initially but then decreases as the rate of its decay surpasses the rate of its formation. The graph for Q typically shows an initial rise, reaches a peak concentration, and then decays towards zero. The exact shape depends on the decay constants $\lambda_1$ and $\lambda_2$.
Mass Behavior of R (Final Product)
Material R is the stable end product. It is formed solely from the decay of Q. Its mass, $M_R(t)$, starts at zero and increases over time as Q decays. Theoretically, if the decay chain goes to completion, the total mass of R will approach the initial mass of P ($M_0$). The graph for R should start at zero and increase over time, eventually leveling off.
Identifying the Correct Figure
The figure representing the time-dependent mass of P, Q, and R must show:
- A curve for P starting high and decreasing exponentially.
- A curve for Q starting at zero, rising to a maximum, and then decreasing towards zero.
- A curve for R starting at zero and increasing towards the initial total mass.
The graph provided in Option A matches this expected behavior for a sequential radioactive decay chain (P → Q → R).
Correct Figure: The figure linked in Option A correctly depicts these characteristics.
Similar Questions
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LIST-I LIST-II A. $^1_0n + ^{235}_{92}U \rightarrow ^{140}_{54}Xe + ^{94}_{38}Sr + 2^1_0n$ I. Chemical reaction B. $2H_2+O_2\rightarrow 2H_2O$ II. Fusion with +ve Q value C. $^1_1H+^2_1H \rightarrow ^3_2He + ^1_0n$ III. Fission D. $^1_1H+^1_1H \rightarrow ^2_1H+^0_1e$ IV. Fusion with -ve Q value Choose the correct answer from the options given below:
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\[\begin{array}{|c|c|c|} \hline A & B & Y \\ \hline 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 1 \\ \hline \end{array}\]Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of x is __________
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(A) the energy of H atom in ground state is same as energy of $He^+$ ion in its first excited state.
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Choose the correct answer from the options given below :A monochromatic light is incident on a metallic plate having work function $\phi$. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point B. The distance between A and B is:
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In the light of the above statements, choose the most appropriate answer from the options given below : - Consider a n-type semiconductor in which $n_e$ and $n_h$ are number of electrons and holes, respectively.
(A) Holes are minority carriers
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Important Questions from Modern Physics
Match the LIST-I with LIST-II
LIST-I LIST-II A. $^1_0n + ^{235}_{92}U \rightarrow ^{140}_{54}Xe + ^{94}_{38}Sr + 2^1_0n$ I. Chemical reaction B. $2H_2+O_2\rightarrow 2H_2O$ II. Fusion with +ve Q value C. $^1_1H+^2_1H \rightarrow ^3_2He + ^1_0n$ III. Fission D. $^1_1H+^1_1H \rightarrow ^2_1H+^0_1e$ IV. Fusion with -ve Q value Choose the correct answer from the options given below:
Choose the correct logic circuit for the given truth table having inputs A and B.
\[\begin{array}{|c|c|c|} \hline A & B & Y \\ \hline 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 1 \\ \hline \end{array}\]Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of x is __________
Considering Bohr's atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of $He^+$ ion in its first excited state.
(B) the energy of H atom in ground state is same as that for $Li^{++}$ ion in its second excited state.
(C) the energy of H atom in ground state is same as that of $He^+$ ion for its ground state.
(D) the energy of $He^+$ ion in its first excited state is same as that for $Li^{++}$ ion in its ground state.
Choose the correct answer from the options given below :A monochromatic light is incident on a metallic plate having work function $\phi$. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point B. The distance between A and B is:
(Given: The magnitude of charge of an electron is $e$ and mass is $m$, $h$ is Planck's constant and $c$ is velocity of light. Take the magnetic field exists throughout the path of electron)
