The wavelngth fo a spectrl line for an electronic transition is inversely related to :

Options

A. a. the number of electron undergoing the transition
B. b. the nucleus charge of the atom
C. c. the difference in the energy of the energy levels involved in the transition
D. d. the velocity of the electron undergoing the transition

Explanation

To solve the question regarding the relationship between the wavelength of a spectral line for an electronic transition and other factors, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Electronic Transition**:
- When an electron transitions between two energy levels (let's say from level n to level m), it either absorbs or emits energy in the form of a photon.

2. **Energy of the Photon**:
- The energy (ΔE) of the photon emitted or absorbed during this transition can be expressed as:
\[ \Delta E = E_n - E_m \]
- Here, \(E_n\) is the energy of the higher energy level (n) and \(E_m\) is the energy of the lower energy level (m).

3. **Relate Energy to Wavelength**:
- The energy of the photon is also related to its wavelength (λ) by the equation:
\[ \Delta E = \frac{hc}{\lambda} \]
- Where:
- \(h\) is Planck's constant,
- \(c\) is the speed of light,
- \(\lambda\) is the wavelength of the emitted or absorbed photon.

4. **Combine the Equations**:
- From the two equations, we can set them equal to each other:
\[ \frac{hc}{\lambda} = E_n - E_m \]

5. **Rearranging the Equation**:
- Rearranging gives us:
\[ \lambda = \frac{hc}{E_n - E_m} \]
- This shows that the wavelength (λ) is inversely proportional to the difference in energy between the two levels (ΔE = E_n - E_m).

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

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

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