Analyze the Assertion (A)

The statement says:

The binding energy per nucleon is practically independent of the mass number $A$ for nuclei with mass numbers between $30$ and $170$.

From the binding energy per nucleon curve, we know that:

• For light nuclei, binding energy per nucleon increases rapidly with $A$.
• For medium-mass nuclei (roughly from $A \approx 30$ to $A \approx 170$), it remains nearly constant, around $8\,\text{MeV}$ per nucleon.
• For very heavy nuclei, it decreases slowly.

Hence, Assertion (A) is true.

Analyze the Reason (R)

The statement says:

Nuclear force is long range.

This is false. Nuclear force is actually a short-range force, effective only over distances of about $1$ to $2\,\text{fm}$.

Because of this short-range nature, each nucleon interacts mainly with only a few nearby nucleons, leading to the saturation property of nuclear forces. This is why the binding energy per nucleon becomes nearly constant for medium-mass nuclei.

Hence, Reason (R) is false.

Conclusion

• Assertion (A): True
• Reason (R): False

Therefore, the correct option is:

$\boxed{\text{A: (A) is true but (R) is false}}$

Comparison with stored correct answer

Stored correct answer: A

My derived answer: A

So, the derived answer agrees with the stored correct answer.