The wavelength of a spectral life for an electronic transition inversely proportional to:

Options

A. Number of electrons undergoing transition
B. The nuclear charge of the atom
C. Velocity of an electron undergoing transition
D. The difference in the energy level involved in the transition.

Answer

To solve the question regarding the wavelength of a spectral line for an electronic transition and what it is inversely proportional to, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Electronic Transition**:
- An electronic transition occurs when an electron moves between two energy levels in an atom. This transition can result in the emission or absorption of a photon.

2. **Energy of the Photon**:
- The energy (E) of the photon emitted or absorbed during this transition can be expressed using the formula:
\[ E = \frac{hc}{\lambda} \]
where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of the emitted or absorbed photon.

3. **Energy Difference Between Levels**:
- The energy difference (\(\Delta E\)) between the two energy levels involved in the transition is given by:
\[ \Delta E = E_2 - E_1 \]
- Thus, the energy of the photon can also be expressed as:
\[ E = \Delta E \]

4. **Relating Wavelength to Energy Difference**:
- From the equations above, we can rearrange the formula for energy to express wavelength in terms of the energy difference:
\[ \lambda = \frac{hc}{\Delta E} \]
- This shows that the wavelength (\(\lambda\)) is inversely proportional to the energy difference (\(\Delta E\)) between the two energy levels.

5. **Conclusion**:
- Therefore, the wavelength of a spectral line for an electronic transition is inversely proportional to the difference in the energy levels involved in the transition.

### Final Answer:
The wavelength of a spectral line for an electronic transition is inversely proportional to the difference in the energy levels involved in the transition (Option D).

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