Q: The mass defect ($\Delta m$) of a nucleus is calculated by:

$\Delta m = \text{sum of masses of nucleons} - \text{mass of nucleus}$

Q: Which of the following is the correct conversion factor to calculate nuclear binding energy from mass defect in amu?

$1 \text{ amu} = 931 \text{ MeV}$

Q: If $1 \text{ amu} = 1.66 \times 10^{-27} \text{ kg}$ and $c = 3.00 \times 10^8 \text{ m/s}$, what is the energy equivalent of $1 \text{ amu}$ in joules?

$E = 1.66 \times 10^{-27} \times (3.00 \times 10^8)^2 = 1.494 \times 10^{-10}$ J

Question 1

Which of the following best describes nuclear binding energy?

Accepted Answer

It is the energy required to break a nucleus into its individual protons and neutrons.

Question 2

The mass defect ($\Delta m$) of a nucleus is calculated by:

Accepted Answer

$\Delta m = 	ext{sum of masses of nucleons} - 	ext{mass of nucleus}$

Question 3

Given the nuclear binding energy formula $E = \Delta m c^2$, what does $c$ represent?

Accepted Answer

The speed of light in a vacuum

Question 4

If the atomic mass of beryllium-10 is 10.012937 amu, and the sum of the masses of its protons and neutrons is 10.072277 amu, what is the mass defect ($\Delta m$) in amu?

Accepted Answer

$\Delta m = 0.05934$ amu

Question 5

Which of the following is the correct conversion factor to calculate nuclear binding energy from mass defect in amu?

Accepted Answer

$1 	ext{ amu} = 931 	ext{ MeV}$

Question 6

A nucleus has a mass defect of $0.005$ amu. What is its binding energy in MeV?

Accepted Answer

$0.005 	imes 931 = 4.655$ MeV

Question 7

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

Accepted Answer

The missing mass is converted to energy that binds the nucleons together.

Question 8

In the reaction $2\ ^1	ext{H} + 2\ ^1	ext{n} ightarrow ^4	ext{He}$, what is the total number of nucleons before and after the reaction?

Accepted Answer

Before: 4, After: 4

Question 9

A scientist is studying the isotope calcium-41, which has a mass of 40.962278 amu. If the sum of the masses of its protons and neutrons is 41.000000 amu, what is the mass defect?

Accepted Answer

$41.000000 - 40.962278 = 0.037722$ amu

Question 10

Which of the following best describes the practical importance of nuclear binding energy in medical applications?

Accepted Answer

It helps select isotopes for diagnostic imaging and cancer treatment.

Question 11

If the mass defect for a helium-4 nucleus is $0.030$ amu, what is its binding energy in MeV?

Accepted Answer

$0.030 	imes 931 = 27.93$ MeV

Question 12

Which equation correctly relates mass defect and binding energy?

Accepted Answer

$E = \Delta m 	imes c^2$

Question 13

A nucleus has a binding energy of $8.0$ MeV. What is the mass defect in amu?

Accepted Answer

$8.0 / 931 = 0.00859$ amu

Question 14

Which of the following is NOT a step in calculating the nuclear binding energy of an isotope?

Accepted Answer

Multiply the atomic number by Avogadro's number.

Question 15

Why is the mass defect always a positive value for stable nuclei?

Accepted Answer

Because energy is released and mass is lost when nucleons bind together.

Question 16

If $1 	ext{ amu} = 1.66 	imes 10^{-27} 	ext{ kg}$ and $c = 3.00 	imes 10^8 	ext{ m/s}$, what is the energy equivalent of $1 	ext{ amu}$ in joules?

Accepted Answer

$E = 1.66 	imes 10^{-27} 	imes (3.00 	imes 10^8)^2 = 1.494 	imes 10^{-10}$ J

Nuclear Binding Energy: Mass Defect and Energy Conversion

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