Three energy levels L₁, L₂ and L₃ of a hydrogen atom correspond to increasing values of energy i.e., Eₗ₁ < Eₗ₂ < Eₗ₃, if the wavelength corresponding to the transitions L₃ to L₂, L₂ to L₁ and L₃ to L₁ are λ₃, λ₂ and λ₁ respectively then,

• A. λ₃ = λ₁ + λ₂
• B. λ₁ = λ₂λ₃ / (λ₂ + λ₃)
• C. λ₁ = λ₂ + λ₃
• D. λ₁ = λ₂λ₃ / (λ₂ - λ₃)

The energy levels of a hydrogen atom are quantized, meaning that electrons can only exist in specific energy states. When an electron transitions between these levels, it emits or absorbs light of a certain wavelength, which is related to the energy difference between the levels.

Understanding Wavelength Relationships

In this context, the wavelengths (λ) associated with the energy levels can be analyzed using the following relationships:

• Option A: λ₃ = λ₁ + λ₂
• Option B: λ₁ = λ₂λ₃ / (λ₂ + λ₃)
• Option C: λ₁ = λ₂ + λ₃
• Option D: λ₁ = λ₂λ₃ / (λ₂ - λ₃)

Evaluating the Options

To determine which equation is correct, we need to consider the principles of energy transitions in hydrogen. The correct relationship typically involves the energy differences between the levels, which can be expressed in terms of wavelengths.

After analyzing the options, the correct relationship is:

Correct Answer

The correct choice is Option B: λ₁ = λ₂λ₃ / (λ₂ + λ₃). This equation reflects how the wavelengths relate to the energy differences between the levels in a hydrogen atom.