Question

The radiation corresponding to $3 \rightarrow 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3 \times 10^{-4}\, T$. If the radius of the largest circular path followed by these electrons is $10.0\, mm$, the work function of the metal is close to :

• A. $1.8\, eV$
• B. $1.1\, eV$
• C. $0.8\, eV$
• D. $1.6\, eV$

Answer 1

Answer: (B)

$r= \frac{m v}{q B} $
$=\frac{\sqrt{2 m e V}}{e B} $
$=\frac{1}{B} \sqrt{\frac{2 m}{e} V} $
$=V=\frac{B^{2} r^{2} e}{2 m}=0.8 \,V$
For transition between 3 to 2 ,
$E =13.6\left(\frac{1}{4}-\frac{1}{9}\right) $
$=\frac{13.6 \times 5}{36}=1.88 \,eV$
Work function $=1.88 \,eV -0.8\, eV$
$=1.08 \,eV =1.1 \,eV$