Q: Which equation correctly represents the mass deficit ($$\Delta m) $$for a nucleus $$^A_ZX$$?

$$\Delta m = Z \times m_{^1_1H} + N \times m_{^1_0n} - m_{^A_ZX}$$

Q: A sample contains $$5.70 \times 10$$^{12}$$ atoms of a radioactive isotope and has an activity of 78.4$ Bq. What is the decay constant $$\lambda$$?

$$1.38 \times 10$$^{-11}$$\ \text{s}^{-1}$$

Q: What is the half-life $$T_{1/2} of a $$radioactive isotope if its decay constant is $$\lambda = 1.38 \times 10$$^{-11}$$\ \text{s}^{-1}$$?

$$T_{1/2} = \frac{0.693}{1.38 \times 10$$^{-11}$$}\ \text{s}$$

Question 1

Which of the following best explains why the mass of a nucleus is less than the sum of the masses of its individual nucleons?

Accepted Answer

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

Question 2

Given the atomic mass of $$^4_2He is 4.0026 u $$and the combined mass of two protons and two neutrons is 4.0330 u, what is the binding energy of the helium nucleus? ($$1\ 	ext{u} = 931.5\ 	ext{MeV}/c^2$)

Accepted Answer

$$28.3\ 	ext{MeV}$$

Question 3

Which equation correctly represents the mass deficit ($$\Delta m) $$for a nucleus $$^A_ZX$$?

Accepted Answer

$$\Delta m = Z 	imes m_{^1_1H} + N 	imes m_{^1_0n} - m_{^A_ZX}$$

Question 4

A Geiger counter detects radiation by which of the following mechanisms?

Accepted Answer

Ionization of gas molecules by incoming radiation, producing a current pulse.

Question 5

In the decay $$^{238}_{92}U \$$rightarrow ^{234}$$_{90}Th + ^4$_2He$$, what type of radioactive decay is occurring?

Accepted Answer

Alpha decay

Question 6

Which of the following statements about the Q-value of a nuclear reaction is correct?

Accepted Answer

If $$Q \u003e 0$$, the reaction is exothermic and releases kinetic energy.

Question 7

A smoke detector uses a radioactive source to ionize air. What happens when smoke enters the detector?

Accepted Answer

The current decreases, triggering the alarm.

Question 8

Which of the following best describes beta-minus ($$\beta^-) $$decay?

Accepted Answer

A neutron in the nucleus transforms into a proton, emitting an electron and an antineutrino.

Question 9

Why was the neutrino hypothesized in beta decay?

Accepted Answer

To account for the missing energy and momentum in beta decay.

Question 10

Which equation describes the exponential decay of radioactive nuclei?

Accepted Answer

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

Question 11

A sample contains $$5.70 	imes 10$$^{12}$$ atoms of a radioactive isotope and has an activity of 78.4$ Bq. What is the decay constant $$\lambda$$?

Accepted Answer

$$1.38 	imes 10$$^{-11}$$\ 	ext{s}^{-1}$$

Question 12

What is the half-life $$T_{1/2} of a $$radioactive isotope if its decay constant is $$\lambda = 1.38 	imes 10$$^{-11}$$\ 	ext{s}^{-1}$$?

Accepted Answer

$$T_{1/2} = \frac{0.693}{1.38 	imes 10$$^{-11}$$}\ 	ext{s}$$

Question 13

A living organism contains $$6.0 	imes 10$$^{10}$$ atoms of $$^{14}C$$ per gram of carbon. If the decay constant is 3.83$$ 	imes $$10^{-12}$$\ 	ext{s}^{-1}$$, what is the activity per gram?

Accepted Answer

$$0.23\ 	ext{Bq}$$

Question 14

A sample of ancient wood has a $$^{14}C$$ activity of $$0.121 Bq $$per gram, compared to $$0.23 Bq $$per gram in living wood. If the half-life of $$^{14}C is$$ $$5730$$ years, what is the approximate age of the sample?

Accepted Answer

$$5300$$ years

Question 15

Which of the following best describes a radioactive decay series?

Accepted Answer

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

Question 16

Which type of radiation is NOT deflected by a magnetic field in the classic experiment with a lead-shielded radioactive source?

Accepted Answer

Gamma ($$\gamma) $$radiation

Question 17

Which of the following isotopes has the longest half-life according to the provided table?

Accepted Answer

$$^{115}_{49}In$$

Question 18

What is the main force responsible for holding nucleons together in the nucleus?

Accepted Answer

The strong nuclear force

Question 19

Which of the following statements about positron ($$\beta^+) $$emission is correct?

Accepted Answer

A proton in the nucleus transforms into a neutron, emitting a positron and a neutrino.

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