Introduction:
Transition in an atom refers to the movement of an electron from one energy level to another. The wave number of a transition is a measure of the energy difference between the initial and final energy levels. In this case, we are looking for a transition in a helium ion (He+) that has the same wave number as the first line in the Balmer series of a hydrogen atom.

Understanding the Balmer series:
The Balmer series is a set of spectral lines that are emitted when an electron in a hydrogen atom transitions from higher energy levels to the second energy level (n=2). The first line in the Balmer series corresponds to the transition from the third energy level (n=3) to the second energy level (n=2).

Transition in a helium ion:
A helium ion (He+) is a helium atom that has lost one electron. It has two protons and only one electron remaining. Similar to hydrogen, the energy levels in a helium ion are quantized, and the electron can transition between these levels by absorbing or emitting energy in the form of photons.

Equation for the wave number:
The wave number (k) of a transition can be calculated using the equation:
k = R * (1/n1^2 - 1/n2^2)
where R is the Rydberg constant, n1 is the initial energy level, and n2 is the final energy level.

Determining the wave number:
To find a transition in a helium ion with the same wave number as the first line in the Balmer series of a hydrogen atom, we need to compare the energy levels involved in both cases.

1. Balmer series of hydrogen:
The first line in the Balmer series corresponds to the transition from the third energy level (n=3) to the second energy level (n=2). Plugging these values into the wave number equation gives us the wave number for this transition in hydrogen.

2. Wave number for a helium ion:
In a helium ion, the energy levels are different due to the presence of two protons in the nucleus. We need to find a transition that has the same wave number as the Balmer series transition in hydrogen.

Conclusion:
In conclusion, to find a transition in a helium ion that has the same wave number as the first line in the Balmer series of a hydrogen atom, we need to compare the energy levels involved in both cases. By calculating the wave numbers using the wave number equation, we can determine the transition in the helium ion that matches the Balmer series transition in hydrogen.