Question

What electron transition in the ${He}^{+}$ spectrum would have the same wavelength as the first Lymann transition of hydrogen?

Answer 1

The $H{e}^{+}$ is a single electron system.The energy level of a system can be written as

$E=R-h\times \frac{Z^2}{n^2}$,

where E=Energy of single atom.

R-h=1.36ev

Z= atomic number,n=1 for H atom and z=2 for $H{e}^{+}$

n= principal quantum number.

The first Lyman transistion of H has energy:

$E\left(H\right)=R-h\times \frac{1-1}{2^2}E\left(H{e}^{+}\right)=R-h\times 2^2(\frac{1}{2^2}-\frac{1}{4^2})$

The electronic transistion will takes place fron n=4 to n=2,the ${He}^{+}$

spectrum have same wavelength as first Lyman transistion of H.