Q: Which formula is used to calculate the nuclear mass of an isotope when the atomic mass is not given?

$\text{Nuclear Mass} = \text{(Number of protons)} \times \text{proton mass} + \text{(Number of neutrons)} \times \text{neutron mass}$

Question 1

Which of the following best describes the concept of 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

Given the following masses: neutron = $1.00866$ amu, proton = $1.00727$ amu, electron = $0.00055$ amu, what is the predicted mass of a helium-4 isotope (2 protons, 2 neutrons, 2 electrons)?

Accepted Answer

$4.03196$ amu

Question 3

Which equation correctly relates mass defect ($\Delta m$) to energy ($E$) released during nuclear binding?

Accepted Answer

$E = \Delta m 	imes c^2$

Question 4

A sample of calcium-42 has an atomic mass of $41.96698$ amu. If the predicted mass (sum of subatomic particles) is $42.34982$ amu, what is the mass defect?

Accepted Answer

$0.38284$ amu

Question 5

Why is the actual mass of a nucleus always less than the sum of the masses of its individual protons and neutrons?

Accepted Answer

Because some mass is converted to energy that binds the nucleus together.

Question 6

Calculate the mass defect for oxygen-16, given: 8 neutrons ($1.00866$ amu each), 8 protons ($1.00727$ amu each), 8 electrons ($0.00055$ amu each), and actual atomic mass $15.99491$ amu.

Accepted Answer

$0.13613$ amu

Question 7

Which step is NOT required when calculating the mass defect of an isotope?

Accepted Answer

Subtracting the mass of electrons from the atomic mass.

Question 8

If the mass defect of a nucleus is $0.005$ amu, what is the energy equivalent released during its formation? (Use $1$ amu $= 1.66054 	imes 10^{-27}$ kg, $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$7.47 	imes 10^{-13}$ J

Question 9

Which of the following statements about the law of conservation of mass-energy is correct?

Accepted Answer

Mass and energy can be interconverted, but their total sum remains constant.

Question 10

A nuclear reaction releases $2.00 	imes 10^{-12}$ J of energy. What is the corresponding mass defect? ($c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$2.22 	imes 10^{-29}$ kg

Question 11

Which formula is used to calculate the nuclear mass of an isotope when the atomic mass is not given?

Accepted Answer

$	ext{Nuclear Mass} = 	ext{(Number of protons)} 	imes 	ext{proton mass} + 	ext{(Number of neutrons)} 	imes 	ext{neutron mass}$

Question 12

A student calculates the predicted mass of a carbon-14 isotope as $14.11154$ amu, but the actual atomic mass is $14.00324$ amu. What is the mass defect?

Accepted Answer

$0.10830$ amu

Question 13

Which of the following best explains why nuclear binding energy is important in medical imaging techniques such as PET scans?

Accepted Answer

It determines the energy released when isotopes decay, which is detected by imaging equipment.

Question 14

If a nucleus has a mass defect of $0.008$ amu, what is the binding energy in MeV? ($1$ amu $= 931.5$ MeV)

Accepted Answer

$7.45$ MeV

Question 15

Which of the following is a direct consequence of the mass defect in atomic nuclei?

Accepted Answer

The release of energy during nuclear fusion and fission.

Question 16

A nucleus contains 6 protons and 8 neutrons. Using proton mass $1.00727$ amu and neutron mass $1.00866$ amu, what is the predicted mass (ignore electrons)?

Accepted Answer

$14.06790$ amu

Question 17

Which of the following is NOT a step in calculating the mass defect for an isotope?

Accepted Answer

Multiplying the mass defect by the speed of light.

Question 18

If the mass defect for a nucleus is $0.010$ amu, what is the equivalent energy in joules? ($1$ amu $= 1.66054 	imes 10^{-27}$ kg, $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$1.50 	imes 10^{-12}$ J

Question 19

Which of the following best describes the relationship between mass defect and nuclear stability?

Accepted Answer

A larger mass defect generally indicates a more stable nucleus due to higher binding energy.

Mass Defect and Energy-Mass Conversion in Nuclear Chemistry

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