A certain electronic transition from an excited state to the ground state of the Hydrogen atom in one or more steps gives rise of 3 lines in the ultra violet region of the spectrum.

How many lines does this transition produce in the Infra red region of the spectrum?

1) 1

2) 2

3) 3

4) 4

To determine how many lines are produced in the infrared region of the spectrum from a transition in the hydrogen atom, we first need to understand the concept of electronic transitions and the associated spectral lines. The transitions between energy levels in hydrogen can be categorized into different series based on the final energy level of the electron. The series relevant to your question are the Lyman series (ultraviolet), Balmer series (visible), and Paschen series (infrared).

Understanding Electronic Transitions

When an electron in a hydrogen atom transitions from a higher energy level to a lower one, it emits a photon, which corresponds to a specific wavelength of light. The number of spectral lines produced during these transitions depends on the initial and final energy levels involved.

Analyzing the Given Transition

You mentioned that a certain transition from an excited state to the ground state produces three lines in the ultraviolet region. This indicates that the transition involves multiple steps, where the electron moves through various energy levels before reaching the ground state (n=1).

• If we denote the initial excited state as n=4, the transitions could be:
• n=4 to n=3
• n=3 to n=2
• n=2 to n=1
• This results in three distinct transitions, hence three lines in the ultraviolet region.

Finding the Infrared Lines

Now, let’s consider the transitions that would occur in the infrared region. The Paschen series corresponds to transitions that end at n=3. If we take the same initial state of n=4, the possible transitions to n=3 would be:

• n=4 to n=3
• n=3 to n=3 (no transition, as it remains in the same level)
• n=2 to n=3 (not applicable for this case)

However, if we consider transitions from n=5 to n=3, we would have:

• n=5 to n=3
• n=4 to n=3
• n=3 to n=3 (no transition)
• n=2 to n=3 (not applicable)

Thus, from the initial excited state of n=4, we can only have one transition that produces a line in the infrared region, which is n=4 to n=3.

Conclusion

Therefore, the number of lines produced in the infrared region from this transition is 1. The correct answer to your question is option 1.