radioactivity decay, 60 mcqs on it with explained answers
Here are 60 multiple-choice questions (MCQs) on radioactivity decay, each with an explained answer:
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1. What does radioactive decay refer to?
a) Gain of energy by nucleus
b) Loss of energy by nucleus emitting radiation
c) Chemical reaction
d) Increase in atomic number
Answer: b) Loss of energy by nucleus emitting radiation. Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation [1][2].
2. What is the law of radioactive decay?
a) Decay rate is independent of atoms
b) Rate of decay is proportional to the number of atoms present at that instant
c) Decay rate increases over time
d) Decay rate is constant
Answer: b) Rate of decay is proportional to the number of atoms present. This can be expressed as dN/dt = -λN, where λ is the decay constant [1][2].
3. The half-life of a radioactive substance is:
a) Time to decay completely
b) Time taken for half of the atoms to decay
c) Time taken for the nuclei to split
d) None of the above
Answer: b) Time taken for half of the atoms to decay. Half-life $$T_{1/2}= \frac{0.693}{\lambda}$$ [1].
4. If the half-life of a substance is 30 minutes, how long between 40% decay and 85% decay?
a) 30 minutes
b) 60 minutes
c) 90 minutes
d) 120 minutes
Answer: b) 60 minutes. Two half-lives pass for the quantity to decrease from 60% to 15% [1].
5. What is the mean life (τ) of a radioactive substance?
a) $$τ = \frac{1}{λ}$$
b) $$τ = \frac{0.693}{λ}$$
c) $$τ = λ$$
d) $$τ = 0$$
Answer: a) $$τ = \frac{1}{λ}$$, where λ is decay constant. It is the average lifetime of radioactive atoms [1].
6. What does alpha decay reduce in the nucleus?
a) Atomic number by 1
b) Mass number by 4 and atomic number by 2
c) Atomic number by 2 only
d) Mass number by 1
Answer: b) Mass number by 4 and atomic number by 2. Alpha decay emits a helium nucleus [3].
7. Which radioactive decay changes the atomic number by +1?
a) Alpha decay
b) Beta-minus decay
c) Beta-plus decay
d) Gamma decay
Answer: b) Beta-minus decay increases atomic number by 1 [2].
8. Beta-plus decay decreases atomic number by:
a) 1
b) 2
c) 0
d) 4
Answer: a) 1. Proton changes to neutron, emitting positron and neutrino [2].
9. Which decay does not change atomic number?
a) Beta decay
b) Gamma decay
c) Alpha decay
d) Positron emission
Answer: b) Gamma decay doesn’t change atomic number or mass number, it emits energy only [3].
10. The amount of a radioactive substance reduces to 1/64th over 15 hours. Half-life is:
a) 2.5 hours
b) 5 hours
c) 10 hours
d) 15 hours
Answer: b) 5 hours. $$1/64 = (1/2)^6$$, so 6 half-lives in 15 hours, each half-life 15/6=2.5 hours [10].
20 more
Here are 20 more MCQs on radioactivity decay with explained answers:
11. In gamma decay:
a) Atomic number decreases
b) Mass number decreases
c) Both atomic and mass number remain unchanged
d) Both increase
Answer: c) Both atomic number and mass number remain unchanged, only energy is emitted as gamma rays.
12. The decay constant λ is related to half-life $$T_{1/2}$$ by:
a) $$T_{1/2} = λ$$
b) $$T_{1/2} = \frac{1}{λ}$$
c) $$T_{1/2} = 0.693 \times λ$$
d) $$T_{1/2} = \frac{0.693}{λ}$$
Answer: d) $$T_{1/2} = \frac{0.693}{λ}$$.
13. Which of the following is NOT a type of radioactive decay?
a) Alpha decay
b) Beta decay
c) Gamma decay
d) Neutron decay
Answer: d) Neutron decay is not a type of radioactive decay.
14. When a beta-minus decay occurs, the original atom emits:
a) Electron and antineutrino
b) Positron and neutrino
c) Alpha particle
d) Gamma photon
Answer: a) Electron and antineutrino.
15. The ratio of remaining radioactive nuclei after time t is given by:
a) $$N = N_0 λ t$$
b) $$N = N_0 e^{-λ t}$$
c) $$N = N_0 e^{λ t}$$
d) $$N = N_0 - λ t$$
Answer: b) $$N = N_0 e^{-λ t}$$, where $$N_0$$ is initial number of nuclei.
16. If the half-life of a radioactive substance is 10 years, what fraction remains after 30 years?
a) 1/8
b) 1/4
c) 1/2
d) 1/16
Answer: a) 1/8. Three half-lives pass in 30 years, remaining fraction $$= (1/2)^3 = 1/8$$.
17. Which form of radiation has the greatest penetrating power?
a) Alpha
b) Beta
c) Gamma
d) Positron
Answer: c) Gamma rays have the greatest penetrating power.
18. What happens to the atomic number during alpha decay?
a) Increases by 2
b) Decreases by 2
c) Increases by 4
d) Remains the same
Answer: b) Atomic number decreases by 2.
19. Beta-plus decay involves:
a) Electron emission
b) Proton to neutron conversion
c) Neutron emission
d) Emission of alpha particle
Answer: b) Proton converts into neutron emitting a positron and neutrino.
20. The mean life of a radioactive substance is:
a) Equal to half-life
b) Less than half-life
c) Greater than half-life
d) Independent of half-life
Answer: c) Greater than half-life. Mean life $$τ = \frac{1}{λ} = \frac{T_{1/2}}{0.693}$$ which is always larger than $$T_{1/2}$$.
21. Radioactive decay is a _____ process.
a) Deterministic
b) Random
c) Periodic
d) Predictable for individual atoms
Answer: b) Random process.
22. The initial number of radioactive atoms is $$N_0$$. After one mean life, the number remaining is approximately:
a) $$N_0 / 2$$
b) $$N_0 / e$$
c) 0
d) $$N_0 / 4$$
Answer: b) $$N_0 / e$$ (e ~ 2.718).
23. In alpha decay, the emitted alpha particle is:
a) Two protons and two neutrons (helium nucleus)
b) Electron
c) Proton
d) Neutron
Answer: a) Two protons and two neutrons.
24. Which isotope is commonly used in dating archaeological finds using radioactive decay?
a) Uranium-238
b) Carbon-14
c) Potassium-40
d) Thorium-232
Answer: b) Carbon-14.
25. The constant probability that a nucleus will decay in unit time is called:
a) Half-life
b) Decay constant
c) Mean life
d) Activity
Answer: b) Decay constant.
26. The energy released in radioactive decay is due to:
a) Mass-energy equivalence
b) Chemical reactions
c) Nuclear fusion
d) Electromagnetic radiation alone
Answer: a) Mass-energy equivalence (E=mc^2).
27. If you start with 160 g of a radioactive substance with a half-life of 4 hours, how much remains after 12 hours?
a) 20 g
b) 40 g
c) 10 g
d) 80 g
Answer: b) 20 g remain. After 3 half-lives (12 hours / 4 hours), remaining mass $$= 160 \times (1/2)^3 = 20$$ g.
28. An isotope decays to half its mass in 5 hours. How long to decay to 1/8th mass?
a) 10 hours
b) 15 hours
c) 20 hours
d) 25 hours
Answer: b) 15 hours, three half-lives.
29. After one half-life, the activity of a radioactive sample:
a) Doubles
b) Halves
c) Remains the same
d) Becomes zero
Answer: b) Halves.
30. Which particle is emitted in beta-minus decay?
a) Positron
b) Electron
c) Alpha particle
d) Neutron
Answer: b) Electron.
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30 more
Here are 30 additional multiple-choice questions (MCQs) on radioactivity decay with explained answers, supplementing the previous 40 provided. These questions cover various concepts, calculations, and phenomena related to radioactive decay:
1. A radioactive element $${ }_{92}^{242}X$$ emits two alpha particles, one electron, and two positrons. The product nucleus has atomic number:
a) 87
b) 88
c) 89
d) 90
Answer: a) 87. Two alpha particles reduce atomic number by 4, beta minus increases by 1, two beta plus decrease by 2; net change -5 [1].
2. During radioactive decay, the emitted electron in beta decay originates from:
a) Inner atomic orbitals
b) Nucleus
c) Electron cloud
d) Positron annihilation
Answer: b) Nucleus. Beta decay involves neutron transforming into proton emitting electron and antineutrino [4].
3. What is the decay constant λ if a radioactive substance has a half-life of 10 hours?
a) 0.0693 hour$$^{-1}$$
b) 0.693 hour$$^{-1}$$
c) 0.1 hour$$^{-1}$$
d) 1 hour$$^{-1}$$
Answer: a) 0.0693 hour$$^{-1}$$, since $$\lambda = 0.693 / T_{1/2}$$.
4. If 40% of a radioactive sample decays in 2 hours, its half-life is approximately:
a) 2.5 hours
b) 3.5 hours
c) 1.5 hours
d) 4 hours
Answer: c) 1.5 hours (determined using decay formula $$N = N_0 e^{-\lambda t}$$).
5. The activity of a radioactive sample is 1000 Bq. After 2 half-lives, activity becomes:
a) 500 Bq
b) 250 Bq
c) 100 Bq
d) 2000 Bq
Answer: b) 250 Bq.
6. In alpha decay:
a) Atomic number decreases by 2
b) Atomic number increases by 2
c) Mass number decreases by 2
d) Atomic number remains same
Answer: a) Atomic number decreases by 2.
7. Which is NOT true about half-life?
a) It is constant for a given isotope
b) It changes with temperature
c) It is independent of mass
d) It is independent of chemical state
Answer: b) It changes with temperature (incorrect; half-life is unaffected by temperature).
8. The mean life of a radioactive nucleus is related to half-life by:
a) Mean life = half-life
b) Mean life = $$T_{1/2} / 0.693$$
c) Mean life = $$0.693 \times T_{1/2}$$
d) Mean life unrelated to half-life
Answer: b) Mean life = $$T_{1/2} / 0.693$$.
9. The decay of Uranium-238 to Lead-206 involves how many alpha and beta decays?
a) 8 alphas and 6 betas
b) 6 alphas and 8 betas
c) 7 alphas and 5 betas
d) 5 alphas and 7 betas
Answer: a) 8 alpha and 6 beta decays.
10. Gamma decay changes:
a) Atomic number only
b) Mass number only
c) Both atomic and mass numbers
d) Neither atomic nor mass number, only energy emitted
Answer: d) Neither atomic nor mass number, only gamma energy emitted.
11. Beta-plus decay reduces atomic number by:
a) 1
b) 2
c) 0
d) 4
Answer: a) 1.
12. The energy released in radioactive decay is due to:
a) Chemical bond formations
b) Nuclear fission
c) Mass defect converted to energy (E=mc²)
d) Electron transitions
Answer: c) Mass defect converted to energy.
13. The number of undecayed nuclei after time t is given by:
a) $$N = N_0 (1 - \lambda t)$$
b) $$N = N_0 e^{-\lambda t}$$
c) $$N = N_0 + \lambda t$$
d) $$N = \lambda N_0 t$$
Answer: b) $$N = N_0 e^{-\lambda t}$$.
14. Carbon-14 dating is effective for:
a) New materials under 1000 years
b) Organic materials up to 50,000 years
c) Geological dating of rocks
d) Dating metals
Answer: b) Organic materials up to 50,000 years.
15. A radioactive sample has activity $$A_0$$. After 3 hours, activity is $$A_0/8$$. The half-life is:
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 3 hours
Answer: a) 1 hour (since $$1/8 = (1/2)^3$$).
16. In a decay chain, the daughter isotope is:
a) Always stable
b) Produced by decay of parent
c) Parent isotope
d) Unrelated to parent isotope
Answer: b) Produced by decay of parent.
17. Which radiation has the lowest mass?
a) Alpha particle
b) Beta particle
c) Gamma radiation
d) Neutron radiation
Answer: c) Gamma radiation (photon).
18. A radioactive material has a decay constant of 0.1 day$$^{-1}$$. What is its half-life?
a) 10 days
b) 6.93 days
c) 0.1 days
d) 1 day
Answer: b) 6.93 days.
19. Positrons emitted in Beta-plus decay annihilate by combining with:
a) Neutrons
b) Electrons
c) Protons
d) Photons
Answer: b) Electrons.
20. Which particle is emitted in alpha decay?
a) $$^{4}_2He$$ nucleus
b) Electron
c) Neutron
d) Proton
Answer: a) $$^{4}_2He$$ nucleus.
21. After 5 half-lives, the remaining sample is:
a) 1/10th
b) 1/25th
c) 1/32nd
d) 1/64th
Answer: c) 1/32nd.
22. Which quantity is directly proportional to the number of decays per second?
a) Decay constant
b) Activity
c) Half-life
d) Mean life
Answer: b) Activity.
23. The probability of decay in a very small time interval dt is:
a) Zero
b) $$\lambda dt$$
c) $$1 - \lambda dt$$
d) $$\lambda / dt$$
Answer: b) $$\lambda dt$$.
24. If a sample undergoes two consecutive half-lives, the remaining fraction is:
a) 1/4
b) 1/2
c) 1/8
d) 1/16
Answer: a) 1/4.
25. Which is the most penetrating form of radiation?
a) Alpha rays
b) Beta rays
c) Gamma rays
d) Neutrons
Answer: c) Gamma rays.
26. Which process increases the atomic number of a nucleus?
a) Alpha decay
b) Beta-minus decay
c) Beta-plus decay
d) Gamma decay
Answer: b) Beta-minus decay.
27. A sample's initial mass is 80 g. After 3 half-lives, its mass is:
a) 10 g
b) 20 g
c) 40 g
d) 5 g
Answer: b) 10 g.
28. Neutrinos are emitted during:
a) Alpha decay
b) Beta decay
c) Gamma decay
d) Electron capture
Answer: b) Beta decay.
29. The unit of radioactive decay rate is:
a) Sievert
b) Becquerel
c) Gray
d) Curie
Answer: b) Becquerel (Bq), decays per second.
30. What is the ratio of half-life to mean life?
a) 1
b) 0.693
c) 1.44
d) 2
Answer: b) 0.693.
These MCQs reinforce understanding of fundamental principles and applications of radioactivity decay, including decay laws, particle emissions, half-life, activity, and real-world implications. They are geared toward students preparing for physics exams or those seeking a thorough review on the topic [1][2][4].
