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Radioactivity – problems and solutions

Radioactivity – problems and solutions

1. Based on the figure below, radioactive activity after decay for 13.86 hours is …

Known :Radioactivity – problems and solutions 1

Half-life (T1/2) = 6.93 hours

Time-lapse (t) = 13.86 hours

Wanted: radioactive activity

Solution :

Radioactivity – problems and solutions 2

A = radioactive activity, λ = the decay constant, Nt = The number of radioactive atoms after decaying during a certain time interval, T1/2 = half-life

The decay constant :

Radioactivity – problems and solutions 3

The number of radioactive atoms after decaying during a certain time interval :

Radioactivity – problems and solutions 4

Radioactive activity :

Radioactivity – problems and solutions 5

2. Based on the figure below, after the radioactive substance decays for 15 minutes, then the remaining radioactive substance is …

Solution :Radioactivity – problems and solutions 6

Radioactivity – problems and solutions 7

No = The initial amount of the radioactive atoms

Nt = The final amount of the radioactive atoms after decaying during a certain time interval (t)

t = time-lapse

T 1/2 = half-life

Calculate the Half-life :

Known :

No = 8 grams

Nt = 2 grams

t = 6 minutes

Wanted: half-life (T 1/2)

Solution :

Radioactivity – problems and solutions 8

Calculate the remaining radioactive material :

Known :

The initial amount of the radioactive atoms (No) = 8 grams

Time-lapse (t) = 15 minutes

Half-life (T 1/2) = 3 minutes

Wanted: the remaining radioactive material (Nt)

Solution :

Radioactivity – problems and solutions 9

1. Question: What is radioactivity?

Answer: Radioactivity is the spontaneous emission of particles or energy from the nucleus of an unstable atom.

2. Question: Name three common types of radioactive decay.

Answer: The three common types are alpha (α) decay, beta (β) decay, and gamma (γ) radiation.

3. Question: What is emitted during alpha decay?

Answer: During alpha decay, an alpha particle is emitted, which consists of 2 protons and 2 neutrons (essentially a helium-4 nucleus).

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4. Question: How does the atomic number of an element change during beta-minus (β⁻) decay?

Answer: During beta-minus decay, a neutron changes into a proton, emitting an electron in the process. This increases the atomic number by one.

5. Question: What is gamma radiation?

Answer: Gamma radiation is a high-energy photon emitted from a radioactive atom. It’s electromagnetic radiation, much like X-rays but more energetic.

6. Question: Why is gamma radiation often emitted after other types of decay?

Answer: Gamma radiation is often emitted after other types of decay to release the excess energy from the excited nucleus, returning it to a lower energy state.

7. Question: What’s the difference between half-life and decay constant?

Answer: Half-life is the time taken for half of the radioactive atoms in a sample to decay, while the decay constant represents the probability per unit time that a single atom will decay.

8. Question: How are radioisotopes used in medicine?

Answer: Radioisotopes can be used in medicine for both diagnostic and therapeutic purposes. For instance, technetium-99m is used in imaging, while iodine-131 is used in the treatment of thyroid disorders.

9. Question: What is the principle behind carbon-14 dating?

Answer: Carbon-14 dating is based on measuring the ratio of carbon-14 (a radioactive isotope) to carbon-12 in organic materials. Since carbon-14 decays over time, the ratio can indicate the age of the sample.

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10. Question: What is the difference between fission and fusion in terms of nuclear reactions?

Answer: Fission is the splitting of a heavy nucleus into two or more smaller ones, releasing energy. Fusion, on the other hand, involves combining two light nuclei to form a heavier one, also releasing energy.

11. Question: How does a Geiger counter work?

Answer: A Geiger counter detects radiation by measuring the ionization produced in a Geiger-Müller tube. When radiation passes through the tube, it ionizes gas inside, causing a measurable electrical discharge.

12. Question: What is the function of control rods in nuclear reactors?

Answer: Control rods absorb neutrons, regulating the rate of the nuclear fission reaction in a reactor. By adjusting the position of these rods, the reaction can be sped up, slowed down, or halted altogether.

13. Question: Why is lead used as a shielding material against radiation?

Answer: Lead is dense and can effectively absorb and stop the different types of radioactive emissions, especially gamma rays, protecting individuals and equipment from radiation exposure.

14. Question: How does the concept of binding energy relate to radioactivity?

Answer: Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. In some cases, if rearranging or emitting particles lowers the total binding energy, the nucleus will do so, leading to radioactive decay.

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15. Question: What’s a common unit to measure radioactivity?

Answer: The Becquerel (Bq) is a common unit, representing one decay event per second.

16. Question: How is radon related to radioactivity?

Answer: Radon is a naturally occurring radioactive gas, formed as a decay product of uranium. It can accumulate in buildings and poses a health risk due to its radioactivity.

17. Question: Why is plutonium-239 significant in nuclear power?

Answer: Plutonium-239 can undergo fission and is used both as a fuel in certain types of nuclear reactors and in the production of nuclear weapons.

18. Question: What is neutron activation?

Answer: Neutron activation is the process in which stable isotopes become radioactive after capturing neutrons. The new isotope often decays by emitting beta or gamma radiation.

19. Question: How do tracers work in studying biological processes?

Answer: Radioactive tracers are isotopes that emit radiation and can be tracked as they move through biological systems. By monitoring their movement, researchers can study processes such as metabolic pathways or blood flow.

20. Question: Why are some elements more radioactive than others?

Answer: The stability of an atomic nucleus depends on the balance of protons and neutrons. Elements with nuclei far from a stable balance of these particles tend to be more radioactive, as they undergo decay to reach a more stable state.

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