Assertion (A) : Limiting line is the balmer series has a wavelength of `364.4 nm`
Reason (R ) : Limiting line is obtained for a jump electron from `n = infty`

Options

A. Statement-I is true, Statement-II is true , Statement-II is correct explanation for Statement-I.
B. Statement-I is true, Statement-II is true , Statement-II is NOT a correct explanation for statement-I
C. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that the limiting line of the Balmer series has a wavelength of 364.4 nm. The Balmer series corresponds to electronic transitions in a hydrogen atom where the electron falls to the n=2 energy level from higher energy levels (n > 2).

### Step 2: Identify the Limiting Line
The limiting line in the Balmer series occurs when the electron transitions from an infinite energy level (n = ∞) to the n = 2 energy level. This transition corresponds to the maximum energy difference, resulting in the shortest wavelength in the series.

### Step 3: Use the Rydberg Formula
To find the wavelength of the limiting line, we can use the Rydberg formula for hydrogen:

\[ \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]

Where:
- \( R \) is the Rydberg constant (approximately \( 1.097 \times 10^7 \, \text{m}^{-1} \))
- \( n_1 = 2 \) (the final energy level for the Balmer series)
- \( n_2 = \infty \) (the initial energy level for the limiting line)

### Step 4: Substitute Values into the Formula
Substituting the values into the Rydberg formula:

\[ \frac{1}{\lambda} = R \left( \frac{1}{2^2} - \frac{1}{\infty^2} \right) \]

Since \( \frac{1}{\infty^2} = 0 \):

\[ \frac{1}{\lambda} = R \left( \frac{1}{4} \right) \]

### Step 5: Solve for Wavelength
Now, we can express the wavelength \( \lambda \):

\[ \lambda = \frac{4}{R} \]

Substituting the value of \( R \):

\[ \lambda = \frac{4}{1.097 \times 10^7} \approx 364.4 \, \text{nm} \]

### Step 6: Conclusion
Thus, the assertion is correct as the limiting line of the Balmer series indeed has a wavelength of 364.4 nm. The reason is also correct because the limiting line is obtained when an electron jumps from \( n = \infty \) to \( n = 2 \).

### Final Answer
Both the assertion and the reason are correct, and the reason correctly explains the assertion.

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