Question

Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric field E through a distance of 1.0 m. The electrons are now scattered by an atomic hydrogen sample in ground state. What should be the minimum value of E so that red light of wavelength 656.3 nm may be emitted by the hydrogen ?

Answer 1

The given wavelength in Balmer series. The first line, which requires minimum energy is form

$n_1=3to{n}_2=2$

$\therefore$ The energy should be euql to the energy required for transition from ground state to n =3

i,e. E = 13.6 $[1-\frac{1}{9}]$

= $\frac{13.6\times 8}{9}=12.09eV$

$\therefore$ Minimum valuve of electric field

= 12.09 V/m

= 12.1 V/m