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 the 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 ? If its value is $a \times 6.05 \,eV$. Find the value of $a$.

Answer 1

$\Delta E =\frac{1242\, eV\,nm }{656.3\, nm } $
$\Delta E =1.89 \,eV .$
electrons should be excited to $n =3$
$E _{3}- E _{1}=-1.5+13.6=12.1\, eV$
electron should have atleast $12.1 \,eV$
energy so that on colliding with atom, atom will able to excite to $n =3$
$\therefore $ electrons should be accelerated by
$E =\frac{ V }{ d }=\frac{12.1}{1}=12.1 \,v / m$
$\vec{ E }=12.1\, volt / m$
$12.1 \,Volt / m$