Q: A sample contains $$1.00 \times 10$$^{22}$$ nuclei of $$^{14}C$$, which has a half-life of 5730 years. Given the decay constant $$\lambda = 3.83 \times $$10^{-12}$$ \ $$s^{-1}$$, what is the activity $$A of $$the sample in decays per second?

$$A = N \lambda = 3.83 \times 10$$^{10}$$ decays/s

Question 1

Which of the following statements best explains why the mass of a stable nucleus is less than the sum of the masses of its constituent protons and neutrons?

Accepted Answer

Some of the mass is converted into binding energy, which holds the nucleus together, according to $$E = mc^2$.

Question 2

A nuclide is represented as $$^A_ZX. If a $$nucleus of $$^{226}_{88}Ra$$ undergoes alpha decay, what are the atomic number and mass number of the daughter nucleus?

Accepted Answer

Atomic number 86, mass number 222

Question 3

Which of the following best describes the difference between alpha, beta, and gamma radiation in terms of their physical nature?

Accepted Answer

Alpha rays are helium nuclei, beta rays are electrons, and gamma rays are electromagnetic radiation.

Question 4

The binding energy per nucleon for $$^{56}_{26}Fe is $$calculated to be 8.79 MeV. What does a higher binding energy per nucleon indicate about a nucleus?

Accepted Answer

The nucleus is more stable.

Question 5

Which force is primarily responsible for holding nucleons together in the nucleus, and why do heavier nuclei require more neutrons for stability?

Accepted Answer

The strong nuclear force; extra neutrons help overcome the Coulomb repulsion between protons.

Question 6

A sample contains $$1.00 	imes 10$$^{22}$$ nuclei of $$^{14}C$$, which has a half-life of 5730 years. Given the decay constant $$\lambda = 3.83 	imes $$10^{-12}$$ \ $$s^{-1}$$, what is the activity $$A of $$the sample in decays per second?

Accepted Answer

$$A = N \lambda = 3.83 	imes 10$$^{10}$$ decays/s

Question 7

Which of the following equations correctly relates the number of undecayed nuclei $$N at $$time $$t to $$the initial number $$N_0$$ and the decay constant $$\lambda$$?

Accepted Answer

$$N = N_0$ e$$^{-\lambda t}$$

Question 8

A neutron decays into a proton, electron, and a neutrino. Which conservation law required the existence of the neutrino in beta decay?

Accepted Answer

Conservation of energy and momentum

Question 9

A radioactive sample has a half-life $$T_{1/2}. $$What is the relationship between the half-life and the decay constant $$\lambda$$?

Accepted Answer

$$T_{1/2} = \frac{0.693}{\lambda}$$

Question 10

Which of the following best explains why gamma rays are not deflected by a magnetic field, while alpha and beta rays are?

Accepted Answer

Gamma rays are uncharged photons, while alpha and beta rays are charged particles.

Question 11

A bone fragment contains 200 g of carbon and registers an activity of 16 decays/s. If living matter has $$1.3 	imes 10$$^{-12}$$ of its carbon as $$^{14}C$$ (half-life 5730 yr), what is the most likely reason the bone cannot be dated if it is older than 60,000 years?

Accepted Answer

There is too little $$^{14}C$$ left to measure accurately.

Question 12

Which of the following is a correct statement about conservation laws in nuclear decay?

Accepted Answer

The total number of nucleons is conserved in all types of radioactive decay.

Question 13

Which of the following best describes the process of radioactive dating using carbon-14?

Accepted Answer

Measuring the remaining fraction of $$^{14}C in $$organic material to estimate the time since death.

Question 14

If the mass of a $$^4_2He$$ nucleus is 4.002603 u and the total mass of its constituent protons and neutrons is 4.032980 u, what is the binding energy of the nucleus? (1 u = 931.5 MeV/$$c^2)$$

Accepted Answer

$$28.2$$ MeV

Question 15

Which of the following is true about the strong nuclear force?

Accepted Answer

It is a short-range force that acts only over distances of about $$10^{-15} m.$$

Question 16

Which of the following best describes a decay series?

Accepted Answer

A sequence of radioactive decays where each product is itself radioactive until a stable nucleus is formed.

Question 17

Which of the following is the correct equation for the rate of radioactive decay?

Accepted Answer

$$\frac{dN}{dt} = -\lambda N$$

Question 18

Which of the following is NOT a property of gamma decay?

Accepted Answer

It changes the atomic number of the nucleus.

Question 19

Which of the following best explains why the electron emitted in beta decay is not an orbital electron?

Accepted Answer

It is created during the decay process from the transformation of a neutron into a proton.

Nuclear Physics and Radioactivity: Structure, Forces, and Decay Processes

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