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. the velocty of an electron undergoing transition
D. the difference in the energy involved in the transition

Answer

To solve the question regarding the relationship between the wavelength of a spectral line for an electronic transition and its dependence on energy levels, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Energy Levels**:
- In an atom, electrons occupy specific energy levels. When an electron transitions from a higher energy level (E2) to a lower energy level (E1), it emits energy in the form of electromagnetic radiation.

2. **Determine the Energy Difference**:
- The energy difference (ΔE) between the two levels is given by:
\[ \Delta E = E_2 - E_1 \]

3. **Relate Energy to Frequency**:
- The energy of the emitted photon can also be expressed in terms of its frequency (ν) using Planck's equation:
\[ \Delta E = h \nu \]
- Where \(h\) is Planck's constant.

4. **Relate Frequency to Wavelength**:
- The frequency of the photon is related to its wavelength (λ) by the equation:
\[ \nu = \frac{c}{\lambda} \]
- Where \(c\) is the speed of light.

5. **Combine the Equations**:
- By substituting the expression for frequency into the energy equation, we have:
\[ \Delta E = h \frac{c}{\lambda} \]

6. **Rearranging for Wavelength**:
- Rearranging the equation gives:
\[ \frac{1}{\lambda} = \frac{\Delta E}{hc} \]
- This shows that the wavelength (λ) is inversely proportional to the energy difference (ΔE).

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

### Final Answer:
The wavelength of a spectral line for an electronic transition is inversely proportional to the energy difference between the two energy levels (ΔE).

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