Question

Monochromatic radiation is emitted when the electron in hydrogen atom jumps from the first excited state to the ground state. It is incident on a photosensitive material. The stopping potential is measured to be $3.57$ $V$. The threshold frequency of the material is

• A. $4\times {10}^{15}Hz$
• B. $5\times {10}^{15}Hz$
• C. $1.6\times {10}^{15}Hz$
• D. $2.5\times {10}^{15}Hz$

Answer 1

The correct option is C $1.6\times {10}^{15}Hz$

For hydrogen atom, $E_n$=-$13.6/n^2$ eV
For ground state, $n=1$
$\therefore$ $E_1$= -$13.6/1^2$= -$13.6$ $eV$
For first excited state, $n=2$
$E_2$= -$13.6/2^2$= -$3.4$ $eV$
The energy of the emitted photon when an electron jumps from first excited state to ground state is
$hv$ = $E_2-E_1=-3.4-(-13.6)$
= $10.2$ $eV$
Maximum kinetic energy,
$K_{max}=eV=e\times 3.57V=3.57eV$
According to Einstein's photoelectric equation
$K_{max}=hv-{\varphi }_0$
${\varphi }_0=10.2eV-3.57eV=6.63eV$
Threshold frequency,
$v_0$=$\frac{{\varphi }_0}{h}=\frac{6.63\times 1.6\times {10}^{-19}}{6.63\times {10}^{-34}}=1.6\times {10}^{15}Hz$