Question

Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric field $E$ through a distance of $1.0m$. 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 $656.3nm$ may be emitted by the hydrogen ? If its value is $a\times 6.05eV$. Find the value of $a$.

Answer 1

Answer: 2.00

$\Delta E=\frac{1242eVnm}{656.3nm}$
$\Delta E=1.89eV.$
electrons should be excited to $n=3$
$E_3-E_1=-1.5+13.6=12.1eV$
electron should have atleast $12.1eV$
energy so that on colliding with atom, atom will able to excite to $n=3$
$\therefore$ electrons should be accelerated by
$E=\frac{V}{d}=\frac{12.1}{1}=12.1v/m$
$\vec{E}=12.1volt/m$
$12.1Volt/m$