Question 261: Atoms & Nuclei

Question

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

Accepted Answer

Radius of circular path followed by electron is given by,
$r = {{m\upsilon } \over {qB}} = {{\sqrt {2meV} } \over {eB}} = {1 \over B}\sqrt {{{2m} \over e}V} $
$ \Rightarrow V = {{{B^2}{r^2}e} \over {2m}} = 0.8V$
For transition between $3$ to $2.$
$E = 13.6\left( {{1 \over 4} - {1 \over 9}} ight)$
$ = {{13.6 	imes 5} \over {36}} = 1.88eV$
Work function $ = 1.88eV - 0.8eV$
$ = 1.08eV \approx 1.1eV$

Answer

$1.8$ $eV$

Answer

$1.1$ $eV$

Answer

$0.8$ $eV$

Answer

$1.6$ $eV$

Atoms & Nuclei

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