Nuclear Size, Mass & Composition — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Nuclear Size, Mass & Composition MCQs with step-by-step solutions (21 questions). Part of Structure of Atoms and Nuclei. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Nuclear Size, Mass & Composition · easy · theory
The nucleus of an atom is composed of:
A. Protons and electrons
B. Protons and neutrons ✓ Correct
C. Neutrons and electrons
D. Only protons
Solution: Collectively protons and neutrons are called nucleons.
Q2 — Nuclear Size, Mass & Composition · easy · theory
The mass number $A$, atomic number $Z$ and neutron number $N$ are related by:
A. $A = Z + N$ ✓ Correct
B. $N = A + Z$
C. $A = Z - N$
D. $A = ZN$
Solution: The mass number simply counts the total number of nucleons.
Q3 — Nuclear Size, Mass & Composition · easy · theory
Isotopes of an element are nuclides having:
A. The same atomic number but different mass numbers ✓ Correct
B. The same mass number but different atomic numbers
C. The same number of nucleons and protons
D. The same number of neutrons
Solution: Isotopes are chemically identical but differ in nuclear mass, for example $^{12}\text{C}$ and $^{14}\text{C}$.
Q4 — Nuclear Size, Mass & Composition · medium · theory
Isobars are nuclides having:
A. Identical chemical properties
B. The same mass number but different atomic numbers ✓ Correct
C. The same number of neutrons
D. The same atomic number but different mass numbers
Solution: They are different elements that happen to contain the same total number of nucleons.
Q5 — Nuclear Size, Mass & Composition · medium · theory
Isotones are nuclides having:
A. The same number of protons
B. The same mass number
C. The same number of neutrons ✓ Correct
D. The same binding energy
Solution: For example $^{13}\text{C}$ and $^{14}\text{N}$ each contain seven neutrons.
Q6 — Nuclear Size, Mass & Composition · medium · theory
The radius of a nucleus of mass number $A$ is given by:
A. $R = R_0A^2$
B. $R = R_0A$
C. $R = R_0A^{1/3}$ with $R_0 \approx 1.2\text{ fm}$ ✓ Correct
D. $R = \dfrac{R_0}{A^{1/3}}$
Solution: The cube-root dependence means the nuclear volume is simply proportional to the number of nucleons.
Q7 — Nuclear Size, Mass & Composition · medium · theory
The density of nuclear matter is:
A. Proportional to the atomic number
B. Practically the same for all nuclei ✓ Correct
C. Inversely proportional to the mass number
D. Proportional to the mass number
Solution: Since volume $\propto A$ and mass $\propto A$, the density cancels out at about $2.3 \times 10^{17}\text{ kg/m}^3$.
Q8 — Nuclear Size, Mass & Composition · easy · theory
One atomic mass unit is equivalent to an energy of approximately:
A. $931.5\text{ MeV}$ ✓ Correct
B. $13.6\text{ MeV}$
C. $1.6 \times 10^{-19}\text{ MeV}$
D. $931.5\text{ eV}$
Solution: This conversion follows from $E = mc^2$ and makes nuclear energy calculations straightforward.
Q9 — Nuclear Size, Mass & Composition · medium · numerical
The radius of a nucleus of mass number $27$ is approximately ($R_0 = 1.2\text{ fm}$):
A. $3.6\text{ fm}$ ✓ Correct
B. $32.4\text{ fm}$
C. $1.2\text{ fm}$
D. $4.8\text{ fm}$
Solution: $R = 1.2 \times 27^{1/3} = 1.2 \times 3 = 3.6\text{ fm}$.
Q10 — Nuclear Size, Mass & Composition · medium · numerical
The radius of a nucleus of mass number $64$ is approximately:
A. $4.8\text{ fm}$ ✓ Correct
B. $3.6\text{ fm}$
C. $76.8\text{ fm}$
D. $6.0\text{ fm}$
Solution: $R = 1.2 \times 64^{1/3} = 1.2 \times 4 = 4.8\text{ fm}$.
Q11 — Nuclear Size, Mass & Composition · medium · numerical
The radius of a nucleus of mass number $125$ is approximately:
A. $4.8\text{ fm}$
B. $3.6\text{ fm}$
C. $6.0\text{ fm}$ ✓ Correct
D. $150\text{ fm}$
Solution: $R = 1.2 \times 125^{1/3} = 1.2 \times 5 = 6.0\text{ fm}$.
Q12 — Nuclear Size, Mass & Composition · hard · numerical
The ratio of the radii of two nuclei of mass numbers $27$ and $64$ is:
A. $9 : 16$
B. $4 : 3$
C. $3 : 4$ ✓ Correct
D. $27 : 64$
Solution: $\dfrac{R_1}{R_2} = \left(\dfrac{27}{64}\right)^{1/3} = \dfrac{3}{4}$.
Q13 — Nuclear Size, Mass & Composition · medium · numerical
The volume of a nucleus is proportional to:
A. $A^2$
B. $A^{2/3}$
C. $A$ ✓ Correct
D. $A^{1/3}$
Solution: With $R \propto A^{1/3}$, the volume $\dfrac{4}{3}\pi R^3 \propto A$.
Q14 — Nuclear Size, Mass & Composition · medium · numerical
If the mass number of a nucleus is increased eight times, its radius becomes:
A. Eight times as large
B. Four times as large
C. Half as large
D. Twice as large ✓ Correct
Solution: $R \propto A^{1/3}$, and $8^{1/3} = 2$.
Q15 — Nuclear Size, Mass & Composition · medium · numerical
The nucleus $^{238}_{92}\text{U}$ contains:
A. $146$ protons and $92$ neutrons
B. $92$ protons and $238$ neutrons
C. $238$ protons
D. $92$ protons and $146$ neutrons ✓ Correct
Solution: The neutron number is $A - Z = 238 - 92 = 146$.
Q16 — Nuclear Size, Mass & Composition · easy · numerical
The number of neutrons in a nucleus of mass number $A$ and atomic number $Z$ is:
A. $Z$
B. $\dfrac{A}{Z}$
C. $A - Z$ ✓ Correct
D. $A + Z$
Solution: The protons number $Z$ and the rest of the nucleons are neutrons.
Q17 — Nuclear Size, Mass & Composition · medium · numerical
The radius of a nucleus of mass number $8$ is approximately:
A. $3.6\text{ fm}$
B. $2.4\text{ fm}$ ✓ Correct
C. $9.6\text{ fm}$
D. $1.2\text{ fm}$
Solution: $R = 1.2 \times 8^{1/3} = 1.2 \times 2 = 2.4\text{ fm}$.
Q18 — Nuclear Size, Mass & Composition · hard · numerical
The density of nuclear matter is of the order of:
A. $10^{27}\text{ kg/m}^3$
B. $10^{17}\text{ kg/m}^3$ ✓ Correct
C. $10^3\text{ kg/m}^3$
D. $10^{10}\text{ kg/m}^3$
Solution: It is roughly $2.3 \times 10^{17}\text{ kg/m}^3$, some fourteen orders of magnitude denser than water.
Q19 — Nuclear Size, Mass & Composition · medium · numerical
The three isotopes of hydrogen contain respectively:
A. $1$, $1$ and $1$ neutron
B. $1$, $2$ and $3$ neutrons
C. $0$, $0$ and $1$ neutron
D. $0$, $1$ and $2$ neutrons ✓ Correct
Solution: Protium, deuterium and tritium all have one proton but zero, one and two neutrons.
Q20 — Nuclear Size, Mass & Composition · easy · numerical
An energy of $1\text{ u}$ of mass defect corresponds to:
A. $93.15\text{ MeV}$
B. $9315\text{ MeV}$
C. $1.5\text{ MeV}$
D. $931.5\text{ MeV}$ ✓ Correct
Solution: This is the standard conversion used in all binding energy calculations.
Q21 — Nuclear Size, Mass & Composition · hard · numerical
Two nuclei have mass numbers in the ratio $1 : 8$. The ratio of their nuclear densities is:
A. $1 : 1$ ✓ Correct
B. $8 : 1$
C. $1 : 8$
D. $1 : 2$
Solution: Nuclear density is independent of mass number, since both mass and volume scale as $A$.