Question

From the statements given below :
(A) The angular momentum of an electron in nth orbit is an integral multiple of h.
(B) Nuclear forces do not obey inverse square law.
(C) Nuclear forces are spin dependent.
(D) Nuclear forces are central and charge independent.
(E) Stability of nucleus is inversely proportional to the value of packing fraction.
Choose the correct answer from the options given below :

• A. (A), (B), (C), (D) only
• B. (A), (C), (D), (E) only
• C. (A), (B), (C), (E) only
• D. (B), (C), (D), (E) only

Answer 1

The Correct Option is C

Let's analyze each statement given in the question to determine the correct answer:

• (A) The angular momentum of an electron in nth orbit is an integral multiple of h.
  According to Bohr's model of the atom, the angular momentum of an electron in the nth orbit is quantized and given by \(L = n\hbar = \frac{nh}{2\pi}\). This statement is correct.
• (B) Nuclear forces do not obey inverse square law.
  Nuclear forces are short-range forces and do not decrease with distance as per the inverse square law, which is characteristic of gravitational and electrostatic forces. This statement is correct.
• (C) Nuclear forces are spin dependent.
  Nuclear forces depend on the spin orientation of the nucleons involved, i.e., neutrons and protons, which means they are spin-dependent. This statement is correct.
• (D) Nuclear forces are central and charge independent.
  While nuclear forces are charge independent, they are not necessarily central forces. A central force acts along the line joining the centers of two particles, which is not a valid description for nuclear forces. Thus, this statement is incorrect.
• (E) Stability of the nucleus is inversely proportional to the value of packing fraction.
  The packing fraction is given by the formula: \(\text{Packing fraction} = \frac{\text{(Mass of nucleus)} - \text{(Mass number)}}{\text{(Mass number)}}\). A lower packing fraction generally indicates higher binding energy per nucleon, thus greater stability of the nucleus. Therefore, this statement is correct.

Analyzing the statements, we find that (A), (B), (C), and (E) are the correct statements. Thus, the correct option is:

(A), (B), (C), (E) only

This matches the answer provided, confirming its accuracy.

Answer 2

Let’s analyze each statement:

Statement (A)

The angular momentum of an electron in the \(n^{th}\) orbit being an integral multiple of \(h\) is a true statement. This is based on Bohr’s quantization condition for angular momentum:

\[ L = n\hbar, \quad \text{where } \hbar = \frac{h}{2\pi} \text{ and } n \in \mathbb{Z} \]

Statement (B)

Nuclear forces do not obey the inverse square law. This is true as nuclear forces are short- ranged and much more complex compared to the inverse-square law of gravitational or electrostatic forces.

Statement (C)

Nuclear forces are spin-dependent. This is true, as the nature of nuclear forces changes with the relative spin orientations of nucleons.

Statement (D)

Nuclear forces are central and charge-independent. This statement is false. While nuclear forces are largely charge-independent, they are not purely central forces since they exhibit a dependence on other factors like spin.

Statement (E)

The stability of the nucleus being inversely proportional to the value of the packing fraction is false. The packing fraction, defined as the binding energy per nucleon, is a measure of nuclear stability, and a lower packing fraction generally indicates lower stability, not higher.

Conclusion

The correct statements are (A), (B), (C), and (E). Therefore, the correct option is:

(3) (A), (B), (C), (E) only