A : wavelength for first line of any series of hydrogen spectrum is biggest among all other lines of the same series .
R : Wavelength of spectral line for an electron transition if inversely related to difference in the energy level involved in the transition .

Options

A. IF both assertion & reason are true and the reason is the correct explanation of the assertion then mark
B. IF both assertion & reason are true but the reason is not the correct explanation of the assertion , then mark
C. IF assertion is true statement but reason is false , then mark
D. If both assertion and reason are false statements then mark

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided:

**Assertion (A):** The wavelength for the first line of any series of the hydrogen spectrum is the biggest among all other lines of the same series.

**Reason (R):** The wavelength of a spectral line for an electron transition is inversely related to the difference in the energy levels involved in the transition.

### Step-by-Step Solution:

1. **Understanding the Energy Levels:**
- According to Bohr's model, the energy of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
- Here, \( n \) is the principal quantum number (1, 2, 3, ...).

2. **Calculating Energy Levels:**
- For \( n = 1 \):
\[ E_1 = -\frac{13.6 \, \text{eV}}{1^2} = -13.6 \, \text{eV} \]
- For \( n = 2 \):
\[ E_2 = -\frac{13.6 \, \text{eV}}{2^2} = -3.4 \, \text{eV} \]
- For \( n = 3 \):
\[ E_3 = -\frac{13.6 \, \text{eV}}{3^2} = -1.51 \, \text{eV} \]
- For \( n = 4 \):
\[ E_4 = -\frac{13.6 \, \text{eV}}{4^2} = -0.85 \, \text{eV} \]

3. **Energy Differences for Transitions:**
- The energy difference for a transition from \( n = 2 \) to \( n = 1 \) is:
\[ \Delta E_{2 \to 1} = E_2 - E_1 = -3.4 - (-13.6) = 10.2 \, \text{eV} \]
- The energy difference for a transition from \( n = 3 \) to \( n = 1 \) is:
\[ \Delta E_{3 \to 1} = E_3 - E_1 = -1.51 - (-13.6) = 12.09 \, \text{eV} \]
- The energy difference for a transition from \( n = 4 \) to \( n = 1 \) is:
\[ \Delta E_{4 \to 1} = E_4 - E_1 = -0.85 - (-13.6) = 12.75 \, \text{eV} \]

4. **Wavelength Calculation:**
- The wavelength \( \lambda \) of the emitted photon during a transition is given by:
\[ \lambda = \frac{hc}{\Delta E} \]
- Since \( h \) (Planck's constant) and \( c \) (speed of light) are constants, the wavelength is inversely proportional to the energy difference \( \Delta E \).

5. **Conclusion on Wavelength:**
- The first line of any series corresponds to the transition with the smallest energy difference, which occurs when the electron transitions from the first excited state (n=2) to the ground state (n=1). This results in the longest wavelength.
- Therefore, the assertion (A) is true.

6. **Evaluating the Reason:**
- The reason (R) states that the wavelength is inversely related to the energy difference, which we have confirmed through our calculations.
- Thus, the reason (R) is also true and correctly explains the assertion (A).

### Final Answer:
Both the assertion and the reason are true, and the reason is the correct explanation of the assertion.