Assertion: In n=2, energy of electron in hydrogen like atoms is more compared to n=1
.Reason: Electrostatic potential energy in n=2 is more.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason or true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the given question, we will analyze both the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that "In n=2, the energy of the electron in hydrogen-like atoms is more compared to n=1."

- The energy of an electron in a hydrogen-like atom is given by the formula:
\[ E_n = -\frac{13.6 \text{ eV}}{n^2} \]
- For n=1:
\[ E_1 = -\frac{13.6 \text{ eV}}{1^2} = -13.6 \text{ eV} \]
- For n=2:
\[ E_2 = -\frac{13.6 \text{ eV}}{2^2} = -\frac{13.6 \text{ eV}}{4} = -3.4 \text{ eV} \]

### Step 2: Comparing Energies
Now, we compare \(E_1\) and \(E_2\):
- Since \(-3.4 \text{ eV}\) (for n=2) is greater than \(-13.6 \text{ eV}\) (for n=1), we conclude that:
\[ E_2 > E_1 \]
- Therefore, the assertion is **true**.

### Step 3: Understanding the Reason
The reason states that "Electrostatic potential energy in n=2 is more."

- The electrostatic potential energy (U) for an electron in a hydrogen-like atom is given by:
\[ U = -\frac{k \cdot e^2}{r} \]
where \(r\) is the radius of the nth orbit, which increases with n.
- For hydrogen-like atoms, the potential energy can also be related to the energy:
\[ U_n = 2E_n \]
- Thus, for n=1:
\[ U_1 = 2 \times (-13.6 \text{ eV}) = -27.2 \text{ eV} \]
- For n=2:
\[ U_2 = 2 \times (-3.4 \text{ eV}) = -6.8 \text{ eV} \]

### Step 4: Comparing Potential Energies
Now, we compare \(U_1\) and \(U_2\):
- Since \(-6.8 \text{ eV}\) (for n=2) is greater than \(-27.2 \text{ eV}\) (for n=1), we conclude that:
\[ U_2 > U_1 \]
- Therefore, the reason is also **true**.

### Step 5: Conclusion
Both the assertion and the reason are true, but the reason does not correctly explain the assertion. The assertion is about the energy levels, while the reason discusses potential energy, which is related but not a direct explanation of the assertion.

Thus, the correct answer is that both the assertion and reason are true, but the reason is not the correct explanation for the assertion.

### Final Answer
**Assertion is true, Reason is true, but Reason is not the correct explanation for Assertion.**

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