Question

Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fastest photoelectrons emitted from sodium is $0.73eV$, The work function for sodium is $1.82eV$. Find the quantum numbers of the two levels in the emission of the photon.

• A. $2,4$.
• B. $3,4$.
• C. $4,4$.
• D. $5,4$.

Answer 1

The correct option is A $2,4$.

We know that,

$E_n=-13.6/n^{2}eV/$ atom for $H$ atom

Let the electron jump from $n_2$ to $n$, then

$E_{n_2}-E_{n_1}=-13.6/n_2^2-\left(13.6/n_1^2\right)$

$\Rightarrow 2.55=13.6(1/n_1^2-1/n_2^2)$

$\therefore$ $n_2=4$ and $n_1=2$