(a) A gas of hydrogen atoms is their ground state is bombarded by electrons with kinetic energy 12.5 ev. What emitted wavelengths would you expect to see?
(b) What if the electrons were replaced by photons of same anergy?.

Answer

A, B

Explanation

(a) `E_n - E_1 = 12.5`
`:. -(13.6)/(n^2) + 13.6 = 12.5`
Solving we get, n=3.51
Hence, electon jumps to n=3. so possible lines
are between n = 3 to n=2, n=3 to n = 1 and
between n = 2 n=1
for n=3 to n=2
`DeltaE = E_3 - E_2 = -(13.6)/(9) + (13.6)/(4)`
=1.9 eV
`:. lambda = (12375)/(1.9) Å =6513 Å`
`~~651 nm`
Similarly, other wavelength can also be obtained. (b) `n= 3.51(in option - alpha)`
A photon always transfers its energy completely.
So, it cannot excite the ground state electrons to
n =3 (like and electrons excited it in part -1).