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The radiation corresponding to 32 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of 3×104T. 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
1.6 eV
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B
1.1 eV
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C
1.8 eV
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D
0.8 eV
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Solution

The correct option is B 1.1 eV
When an electron moves in a circular path, then
evB=mv2r r=mveB r=2meVeB or 1B2mVeV=er2B22mstopping potential
V=100×106×1.6×1019×9×1082×9.1×1031 =0.8 V

KE of electron, K=0.8 eV

For transition between 3 to 2,

E=13.6(122132)
E=13.6×536E=1.88 eV

Work fuction,
ϕo=EKmax
=1.890.791.1 eV

Hence, option B is correct.

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