a. What optical transition in the `He^(o+)` spectrum would have the same `lambda` as the first Lyman transition of hydrogen `(n = 2 to n = 1)` ?
b. What is the IP of `He^(Theta)`
What is the radius of the first Bohr orbit for `He^(Theta)` ?

Explanation

`bar v RZ^(2) ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
The first Lyman transition for hydrogen is
`bar v = R ((1)/(1^(2)) - (1)/(2^(2)))` ……(i)
For `He^(o+) ,bar v R(2)^(2)((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`……..(ii)
The `Z^(2)` term can just be compensated by increasing `n_(1)` and `n_(2)` by a factor of `2` each .THe transition in question is thus the transition from `n = 4 to n = 2`
b. The second IP of He is the same as the IP of `He^(Theta)` and the bohr equation may be applied to the griound state of `He^(Theta)` , for which `n = 2 ` and `n= 1` IP (He^(THeta)) = Z^(2) xx IP (H) = 4 xx 13.6 eV = 54.4 eV`
c. `r = (n^(2)a_(0))/(Z) = (0.529 Å)/(2) = 0.264 Å`