QJEEM14Ph50bb: JEE Main 2014 Physics - Class 12 JEEM14Ph50bb Solution: The radiation corresponding to transition of hydrogen atom…

Question

Verified Solution • 2025–26 Session moderate

The radiation corresponding to

3 \to 2

transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field

3 \times {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}} \right)

= {{13.6 \times 5} \over {36}} = 1.88eV

Work function

= 1.88eV - 0.8eV

= 1.08eV \approx 1.1eV

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