The wavelength of a line a spectrum is inversely proportional to

Options

A. Number of electrons
B. Velocity of the electrons
C. Difference in energy levels
D. Momentum of the electrons

Explanation

To solve the question, we need to understand the relationship between the wavelength of light emitted during electronic transitions in an atom and the energy levels involved in these transitions.

### Step-by-Step Solution:

1. **Understanding the Concept**: The wavelength of light emitted (λ) during an electronic transition in an atom is related to the energy difference (ΔE) between the two energy levels involved in the transition.

2. **Energy-Wavelength Relationship**: According to the formula derived from quantum mechanics, the energy difference between two levels is given by:
\[ \Delta E = \frac{hc}{\lambda} \]
where:
- \( \Delta E \) is the energy difference,
- \( h \) is Planck's constant,
- \( c \) is the speed of light,
- \( \lambda \) is the wavelength.

3. **Rearranging the Formula**: From the equation above, we can rearrange it to express the wavelength in terms of energy:
\[ \lambda = \frac{hc}{\Delta E} \]

4. **Understanding Inverse Proportionality**: From the rearranged equation, we can see that the wavelength (λ) is inversely proportional to the energy difference (ΔE). This means as the energy difference increases, the wavelength decreases, and vice versa.

5. **Conclusion**: Therefore, the correct answer to the question is that the wavelength of a line spectrum is inversely proportional to the difference in energy level.

### Final Answer:
The wavelength of a line spectrum is inversely proportional to the difference in energy level.

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