Electromagnetic waves of wavelenglth `1242 Å` are indicdent on a metal of work funcation `2eV`. The target metal is connected to a `5` volt cell, as shown. The electrons pass through hole into a gas of hydrogen atoms in their ground stte. Find the number of spectral lines emitted when hydrogen atoms come back to their ground states after having been excited by the electrons, Assume all excitations in H-atoms from ground state only (`hc = 12420 eVÅ`)

Answer

6

Explanation

`kE_(max) = (12420ÅeV)/(1242Å) - 2eV = 8 eV`

The electrons are emitted with kinetic energy varying from zero to `8 eV`
When acclerated with `5` volt potential difference their energies increases by `5eV`.
Hence hydrogen will get photons of energies in the range from `5` eV to `13 eV`.
So maximum possible transactions are upto `n = 4`, Hence number of spectra lines is `.^(4)C_(2) = 6`