Radioactivity & Decay Law — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Radioactivity & Decay Law MCQs with step-by-step solutions (20 questions). Part of Structure of Atoms and Nuclei. Practise online on Prepizo — no login needed.
▶ Practise Radioactivity & Decay Law online (free)
Questions with solutions
Q1 — Radioactivity & Decay Law · easy · theory
In alpha decay, the mass number and atomic number of the nucleus change by:
A. $-2$ and $-4$ respectively
B. $-4$ and $-2$ respectively ✓ Correct
C. $-4$ and $+2$ respectively
D. $0$ and $+1$ respectively
Solution: An alpha particle carries away two protons and two neutrons.
Q2 — Radioactivity & Decay Law · medium · theory
In beta-minus decay, the mass number and atomic number change by:
A. $-4$ and $-2$ respectively
B. $0$ and $-1$ respectively
C. $0$ and $+1$ respectively ✓ Correct
D. $+1$ and $0$ respectively
Solution: A neutron converts into a proton, an electron and an antineutrino, so $A$ is unchanged while $Z$ rises by one.
Q3 — Radioactivity & Decay Law · easy · theory
In gamma emission, the mass number and atomic number of the nucleus:
A. Both remain unchanged ✓ Correct
B. Both increase
C. Both decrease
D. Change by $-4$ and $-2$
Solution: Gamma emission merely carries away excess energy from an excited nucleus.
Q4 — Radioactivity & Decay Law · easy · theory
The radioactive decay law is expressed as:
A. $N = N_0e^{-\lambda t}$ ✓ Correct
B. $N = N_0\lambda t$
C. $N = \dfrac{N_0}{\lambda t}$
D. $N = N_0e^{\lambda t}$
Solution: The decay is exponential, with $\lambda$ the decay constant characteristic of the nuclide.
Q5 — Radioactivity & Decay Law · easy · theory
The half-life and decay constant of a radioactive nuclide are related by:
A. $T_{1/2} = \dfrac{0.693}{\lambda}$ ✓ Correct
B. $T_{1/2} = \dfrac{1}{\lambda}$
C. $T_{1/2} = 0.693\lambda$
D. $T_{1/2} = \dfrac{\lambda}{0.693}$
Solution: Setting $N = \dfrac{N_0}{2}$ in the decay law gives $T_{1/2} = \dfrac{\ln 2}{\lambda}$.
Q6 — Radioactivity & Decay Law · medium · theory
The mean life of a radioactive nuclide is:
A. $\lambda$ itself
B. $\dfrac{1}{\lambda}$, which is shorter than its half-life
C. $\dfrac{1}{\lambda}$, which is longer than its half-life ✓ Correct
D. Equal to its half-life
Solution: Since $\tau = \dfrac{T_{1/2}}{0.693}$, the mean life exceeds the half-life by about $44\%$.
Q7 — Radioactivity & Decay Law · medium · theory
The activity of a radioactive sample is given by:
A. $\lambda N$ ✓ Correct
B. $\dfrac{\lambda}{N}$
C. $\dfrac{N}{\lambda}$
D. $\lambda N^2$
Solution: It is the number of disintegrations per second, measured in becquerel.
Q8 — Radioactivity & Decay Law · medium · theory
The SI unit of radioactivity is the becquerel, which equals:
A. $3.7 \times 10^{10}$ disintegrations per second
B. One disintegration per minute
C. One disintegration per second ✓ Correct
D. One curie
Solution: The older unit, the curie, equals $3.7 \times 10^{10}\text{ Bq}$.
Q9 — Radioactivity & Decay Law · medium · numerical
The half-life of a radioactive substance is $30\text{ days}$. Its mean life is approximately:
A. $15\text{ days}$
B. $43.3\text{ days}$ ✓ Correct
C. $20.8\text{ days}$
D. $60\text{ days}$
Solution: $\tau = \dfrac{T_{1/2}}{0.693} = \dfrac{30}{0.693} \approx 43.3\text{ days}$.
Q10 — Radioactivity & Decay Law · hard · numerical
The decay rate of a radioactive isotope falls to one-eighth of its initial value in $24\text{ hours}$. Its decay constant is:
A. $\dfrac{\ln 2}{6}\text{ hr}^{-1}$
B. $\dfrac{\ln 2}{8}\text{ hr}^{-1}$ ✓ Correct
C. $\dfrac{\ln 2}{24}\text{ hr}^{-1}$
D. $\dfrac{\ln 2}{3}\text{ hr}^{-1}$
Solution: $\dfrac{1}{8} = \left(\dfrac{1}{2}\right)^3$ means three half-lives in $24\text{ h}$, so $T_{1/2} = 8\text{ h}$ and $\lambda = \dfrac{\ln 2}{8}$.
Q11 — Radioactivity & Decay Law · medium · numerical
The half-life of a radioactive substance is $4\text{ hours}$. The fraction of the original activity remaining after $16\text{ hours}$ is:
A. $\dfrac{1}{8}$
B. $\dfrac{1}{16}$ ✓ Correct
C. $\dfrac{1}{32}$
D. $\dfrac{1}{4}$
Solution: Sixteen hours is four half-lives, so the fraction left is $\left(\dfrac{1}{2}\right)^4 = \dfrac{1}{16}$.
Q12 — Radioactivity & Decay Law · hard · numerical
The half-life of a radioactive sample is $10\text{ days}$. The time for $75\%$ of it to disintegrate is:
A. $15\text{ days}$
B. $25\text{ days}$
C. $20\text{ days}$ ✓ Correct
D. $30\text{ days}$
Solution: If $75\%$ decays, $25\% = \left(\dfrac{1}{2}\right)^2$ remains, so two half-lives have elapsed.
Q13 — Radioactivity & Decay Law · medium · numerical
A sample contains $10^{10}$ radioactive nuclei with decay constant $2 \times 10^{-4}\text{ s}^{-1}$. Its activity is:
A. $2 \times 10^{-14}\text{ disintegrations per second}$
B. $2 \times 10^6\text{ disintegrations per second}$ ✓ Correct
C. $10^6\text{ disintegrations per second}$
D. $5 \times 10^{13}\text{ disintegrations per second}$
Solution: $A = \lambda N = 2 \times 10^{-4} \times 10^{10} = 2 \times 10^6\text{ Bq}$.
Q14 — Radioactivity & Decay Law · hard · numerical
When $^{238}_{92}\text{U}$ decays into $^{206}_{82}\text{Pb}$, the numbers of alpha and beta-minus particles emitted are respectively:
A. $8$ and $6$ ✓ Correct
B. $8$ and $4$
C. $6$ and $8$
D. $10$ and $6$
Solution: Mass number falls by $32$, requiring $8$ alphas. That would drop $Z$ to $76$, so $6$ beta decays are needed to reach $82$.
Q15 — Radioactivity & Decay Law · medium · numerical
The half-life of a radioactive element is $5\text{ years}$. The fraction remaining after $15\text{ years}$ is:
A. $\dfrac{1}{8}$ ✓ Correct
B. $\dfrac{1}{16}$
C. $\dfrac{1}{3}$
D. $\dfrac{1}{4}$
Solution: Fifteen years is three half-lives, leaving $\left(\dfrac{1}{2}\right)^3 = \dfrac{1}{8}$.
Q16 — Radioactivity & Decay Law · medium · numerical
A radioactive nuclide has a half-life of $10\text{ s}$. Its decay constant is approximately:
A. $14.4\text{ s}^{-1}$
B. $6.93\text{ s}^{-1}$
C. $0.693\text{ s}^{-1}$
D. $0.0693\text{ s}^{-1}$ ✓ Correct
Solution: $\lambda = \dfrac{0.693}{T_{1/2}} = \dfrac{0.693}{10} = 0.0693\text{ s}^{-1}$.
Q17 — Radioactivity & Decay Law · easy · numerical
The fraction of a radioactive sample remaining after two half-lives is:
A. $75\%$
B. $12.5\%$
C. $50\%$
D. $25\%$ ✓ Correct
Solution: Each half-life halves the amount: $100\% \to 50\% \to 25\%$.
Q18 — Radioactivity & Decay Law · easy · numerical
The activity of a radioactive sample after one half-life compared with its initial value is:
A. Zero
B. Half ✓ Correct
C. Unchanged
D. One-quarter
Solution: Activity is proportional to the number of undecayed nuclei, which halves in one half-life.
Q19 — Radioactivity & Decay Law · hard · numerical
A radioactive nuclide has a mean life of $\tau$. Its half-life is:
A. $0.693\tau$ ✓ Correct
B. $\tau$
C. $2\tau$
D. $1.44\tau$
Solution: $T_{1/2} = \tau\ln 2 = 0.693\tau$, so the half-life is shorter than the mean life.
Q20 — Radioactivity & Decay Law · hard · numerical
A radioactive sample loses $\dfrac{7}{8}$ of its nuclei in $30\text{ minutes}$. Its half-life is:
A. $15\text{ minutes}$
B. $10\text{ minutes}$ ✓ Correct
C. $7.5\text{ minutes}$
D. $30\text{ minutes}$
Solution: One-eighth remains, which is three half-lives, so $T_{1/2} = \dfrac{30}{3} = 10\text{ minutes}$.