(A) : The energy of electrons is largely determined by its principal quantum number.
(R) : The principal quantum number is a measure of most probable distance of finding the electron around the nucleus

Options

A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
C. (A) is true but (R) is false
D. (A) is false but (R) is true

Answer

To analyze the given assertion (A) and reason (R), we can break down the solution step by step:

### Step 1: Understanding the Assertion (A)
The assertion states that "The energy of electrons is largely determined by its principal quantum number."

- The principal quantum number (n) indicates the energy level of an electron in an atom.
- The energy of an electron in a hydrogen-like atom can be expressed as:
\[ E = -\frac{13.6 \, Z^2}{n^2} \]
where \( Z \) is the atomic number and \( n \) is the principal quantum number.
- As \( n \) increases, the energy becomes less negative, indicating that the electron is at a higher energy level. Thus, the assertion is **true**.

### Step 2: Understanding the Reason (R)
The reason states that "The principal quantum number is a measure of the most probable distance of finding the electron around the nucleus."

- The principal quantum number (n) does indeed relate to the average distance of the electron from the nucleus.
- Higher values of \( n \) correspond to orbitals that are further from the nucleus, indicating that the electron is likely to be found farther away.
- Therefore, this statement is also **true**.

### Step 3: Analyzing the Relationship Between A and R
Now, we need to determine if the reason (R) correctly explains the assertion (A).

- The assertion (A) indicates that the energy of the electron is determined by \( n \), while the reason (R) explains that \( n \) represents the distance of the electron from the nucleus.
- Since the energy of the electron is indeed influenced by its distance from the nucleus (as represented by \( n \)), we can conclude that the reason does explain the assertion.

### Conclusion
Both the assertion (A) and the reason (R) are true, and R is the correct explanation of A. Therefore, the correct answer is:
- **Both A and R are true, and R is the correct explanation of A.**

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