Q: If a radioactive sample has a decay rate $$r = 0.1 Hz $$and an initial number of nuclei $$N_0 = 1000$, what is the expected number of nuclei remaining after t = 10$ seconds?

$$N(10) = 1000 \times e$$^{-1}$$ \approx 368$$

Question 1

Which of the following best describes the atomic number $$Z of a $$nucleus?

Accepted Answer

The number of protons in the nucleus.

Question 2

A nucleus is represented as $$\displaystyle \frac{A}{Z}X. $$What does the symbol $$X$$ stand for?

Accepted Answer

The chemical symbol of the element, determined by the number of protons.

Question 3

Which force is responsible for holding protons and neutrons together in the nucleus despite the repulsive electrostatic force between protons?

Accepted Answer

Strong nuclear force

Question 4

According to the shell model, what is the main reason for the existence of discrete energy levels for nucleons in a nucleus?

Accepted Answer

Nucleons move independently in an average potential due to the strong force.

Question 5

Which type of radioactive decay results in the emission of a $$^4He $$nucleus?

Accepted Answer

Alpha decay

Question 6

A sample contains $$2 	imes 10$$^{12}$$ atoms of $$^{131}$$I, which has a half-life of 8 days. How many atoms remain after 36 hours? Use N(t$$) = $$N_0$$ \left( \frac{1}{2} \$$right)^{t/t_{1/2}$$}$$.

Accepted Answer

$$1.85 	imes 10$$^{12}$$

Question 7

Which of the following statements about binding energy is correct?

Accepted Answer

Binding energy is the energy required to disassemble a nucleus into its nucleons.

Question 8

What is the equation for the number of unstable nuclei remaining at time $$t if $$the initial number is $$N_0$$ and the decay rate is $$r$$?

Accepted Answer

$$N(t) = N_0$ e$$^{-rt}$$

Question 9

Which particle is emitted in beta-minus ($$\beta^-) $$decay?

Accepted Answer

An electron

Question 10

The half-life $$t_{1/2} of a $$radioactive isotope is related to the decay rate $$r by $$which equation?

Accepted Answer

$$t_{1/2} = \frac{\ln(2)}{r}$$

Question 11

Which of the following is true about gamma ($$\gamma) $$radiation?

Accepted Answer

It consists of high-energy photons and is stopped by many centimeters of lead.

Question 12

A $$^{238}_{92}U $$nucleus undergoes alpha decay. What is the resulting daughter nucleus?

Accepted Answer

$$^{234}_{90}Th$$

Question 13

Which process is responsible for the energy production in the Sun?

Accepted Answer

Nuclear fusion of hydrogen nuclei

Question 14

What is the main difference between nuclear fission and nuclear fusion?

Accepted Answer

Fission splits a heavy nucleus; fusion combines two light nuclei.

Question 15

Which equation gives the activity $$R(t) of a $$radioactive sample at time $$t$$?

Accepted Answer

$$R(t) = r N(t)$$

Question 16

Why are neutrinos necessary in beta decay?

Accepted Answer

To conserve momentum and energy.

Question 17

If a radioactive sample has a decay rate $$r = 0.1 Hz $$and an initial number of nuclei $$N_0 = 1000$, what is the expected number of nuclei remaining after t = 10$ seconds?

Accepted Answer

$$N(10) = 1000 	imes e$$^{-1}$$ \approx 368$$

Question 18

Which of the following statements about nuclear stability is correct?

Accepted Answer

There are no stable nuclei with $$Z \u003e 83.$$

Question 19

What is the main reason high-Z nuclei tend to undergo alpha decay?

Accepted Answer

To become more tightly bound and stable by reducing the number of nucleons.

Question 20

Which equation best describes the energy released in an alpha decay?

Accepted Answer

$$\Delta E = (m_X - m_Y - m_{He})c^2$

Nuclear Decay and Radioactivity: Structure, Stability, and Decay Processes

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