Q: A radioactive isotope decays with a rate constant $$k = 0.002 \text{ day}^{-1}. $$What is its half-life?

$$t_{1/2} = \frac{0.693}{0.002} = 346.5 \text{ days}$$

Q: A sample of $$^{60}\text{Co}$$ has an initial activity of 1000 counts per minute. After 10 years, the activity drops to 250 counts per minute. What is the rate constant $$k$$ for this decay?

$$k = -\frac{1}{t} \ln\left(\frac{\text{rate}_t}{\text{rate}_0}\right) = -\frac{1}{10} \ln\left(\frac{250}{1000}\right) = 0.1386 \text{ yr}^{-1}$$

Q: Which of the following is a correct balanced equation for beta-minus decay of $$^{14}_{6}\text{C}$$?

$$^{14}_{6}\text{C} \$$rightarrow ^{14}$$_{7}\text{N} + e$$^{-}$$ + \bar{\nu}_e$$

Q: Calculate the mass defect for $$^{4}_{2}\text{He} ($$alpha particle) given: mass of $$^{4}_{2}\text{He}$$ nucleus = 4.0026 amu, mass of proton = 1.0073 amu, mass of neutron = 1.0087 amu.

Mass defect $$= (2 \times 1.0073 + 2 \times 1.0087) - 4.0026 = 0.0300 \text{ amu}$$

Q: The binding energy per nucleon for a nucleus is calculated using which equation?

$$E = \frac{\Delta m \cdot c^2$}{\text{number of nucleons}}$$

Q: A nuclear reactor uses $$^{235}\text{U}$$ fission. Which of the following best describes the process?

$$^{235}\text{U}$$ absorbs a neutron, splits into two lighter nuclei, and releases additional neutrons and energy.

Question 1

Which of the following best describes the term 'mass defect' in nuclear chemistry?

Accepted Answer

The difference between the mass of a nucleus and the sum of the masses of its constituent protons and neutrons.

Question 2

A radioactive isotope decays with a rate constant $$k = 0.002 	ext{ day}^{-1}. $$What is its half-life?

Accepted Answer

$$t_{1/2} = \frac{0.693}{0.002} = 346.5 	ext{ days}$$

Question 3

Which nuclear decay process increases the N/Z ratio of a nuclide?

Accepted Answer

Beta-minus ($$\beta^-) $$decay

Question 4

Given the following nuclear reaction: $$^{14}_{7}	ext{N} $$+ ^{4}$$_{2}	ext{He} \$$rightarrow ^{17}$$_{8}	ext{O} $$+ ^{1}$$_{1}	ext{H}$$, what type of reaction is this?

Accepted Answer

Nuclear transformation

Question 5

Which of the following statements about the strong force is correct?

Accepted Answer

It binds protons and neutrons together in the nucleus.

Question 6

A sample of $$^{60}	ext{Co}$$ has an initial activity of 1000 counts per minute. After 10 years, the activity drops to 250 counts per minute. What is the rate constant $$k$$ for this decay?

Accepted Answer

$$k = -\frac{1}{t} \ln\left(\frac{	ext{rate}_t}{	ext{rate}_0}ight) = -\frac{1}{10} \ln\left(\frac{250}{1000}ight) = 0.1386 	ext{ yr}^{-1}$$

Question 7

Which of the following is a correct balanced equation for beta-minus decay of $$^{14}_{6}	ext{C}$$?

Accepted Answer

$$^{14}_{6}	ext{C} \$$rightarrow ^{14}$$_{7}	ext{N} + e$$^{-}$$ + \bar{
u}_e$$

Question 8

Which nuclide is most likely to undergo electron capture?

Accepted Answer

A nuclide with a low N/Z ratio

Question 9

Calculate the mass defect for $$^{4}_{2}	ext{He} ($$alpha particle) given: mass of $$^{4}_{2}	ext{He}$$ nucleus = 4.0026 amu, mass of proton = 1.0073 amu, mass of neutron = 1.0087 amu.

Accepted Answer

Mass defect $$= (2 	imes 1.0073 + 2 	imes 1.0087) - 4.0026 = 0.0300 	ext{ amu}$$

Question 10

Which of the following statements about nuclear fission is correct?

Accepted Answer

It involves splitting a heavy nucleus into lighter nuclei, releasing energy.

Question 11

The binding energy per nucleon for a nucleus is calculated using which equation?

Accepted Answer

$$E = \frac{\Delta m \cdot c^2$}{	ext{number of nucleons}}$$

Question 12

Which of the following is NOT a fundamental particle found in the nucleus?

Accepted Answer

Electron

Question 13

A nuclear reactor uses $$^{235}	ext{U}$$ fission. Which of the following best describes the process?

Accepted Answer

$$^{235}	ext{U}$$ absorbs a neutron, splits into two lighter nuclei, and releases additional neutrons and energy.

Question 14

Which equation correctly relates the number of radioactive nuclei at time $$t to $$the initial number?

Accepted Answer

$$\ln\left(\frac{N_t}{N_0$}\right) = -kt$$

Question 15

Which of the following is a real-world application of nuclear fusion?

Accepted Answer

The energy production in stars, including the Sun.

Question 16

A nuclide has a high N/Z ratio. Which decay process is it most likely to undergo?

Accepted Answer

Beta-minus ($$\beta^-) $$decay

Question 17

Which of the following best describes the difference between fission and fusion?

Accepted Answer

Fission splits heavy nuclei; fusion combines light nuclei.

Question 18

A hospital uses $$^{99m}	ext{Tc}$$ for imaging. After 24 hours, only 25% of the original activity remains. What is the half-life?

Accepted Answer

Half-life $$= 12 	ext{ hours}$$

Question 19

Which of the following is the correct symbol for a neutron?

Accepted Answer

$$^{1}_{0}	ext{n}$$

Nuclear Chemistry: Key Concepts and Calculations

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