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

Options

A. Thenumber of electron undergoing the transition
B. The nuclear charge of the atom
C. The difference in the energy of the energy7 levels involoved in the transition
D. The velocity of the undegoing the transition

Explanation

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

### Step 1: Understand the relationship between wavelength and energy
The energy associated with a photon can be expressed using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant,
- \( c \) is the speed of light,
- \( \lambda \) is the wavelength.

### Step 2: Rearranging the equation
From the equation above, we can rearrange it to express wavelength in terms of energy:
\[ \lambda = \frac{hc}{E} \]

### Step 3: Consider electronic transitions
For electronic transitions, the energy difference (\( \Delta E \)) between two energy levels (say \( E_2 \) and \( E_1 \)) can be defined as:
\[ \Delta E = E_2 - E_1 \]

### Step 4: Substitute energy difference into the wavelength equation
Substituting \( \Delta E \) into the wavelength equation gives:
\[ \lambda = \frac{hc}{\Delta E} \]

### Step 5: Identify the relationship
From the rearranged equation, we can see that:
\[ \lambda \propto \frac{1}{\Delta E} \]
This indicates that the wavelength (\( \lambda \)) is inversely proportional to the energy difference (\( \Delta E \)) involved in the electronic transition.

### Conclusion
Thus, the wavelength of a spectral line for an electronic transition is inversely related to the difference in energy involved in the transition.

### Final Answer
The correct answer is that the wavelength of a spectral line for an electronic transition is inversely related to the difference in energy (\( \Delta E \)).

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