A small plate of a metal (work function = 1.17 eV) is placed at a distance of 2 m from a monochromatic light source of wavelength 4800 Å and power 1.0 watt. The light falls normally on the plate. If a constant magnetic field of strength 10 4 Tesla is applied parallel to metal surface. Find the radius (in cm) of the largest circular path followed by the emitted photo electrons.
Text Solution
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(4)
Sol. Energy of incident photon is eV is
E = 
eV = 2.58 eV = 2.58 × 1.6 × 10 –19 J
= 4.125 × 10 –19 J.
The rate of emission of photon from source
r = I /E = 
= 2.424 × 10 18 /sec
No. of photon striking per square metal per sec on the plate
= 
= 4.82 × 10 16 m –2 sec –1 The maximum kinetic energy of the photo electrons emitted from the plate having work function φ = 1.17 eV is given by
KE max = E – φ = 2.58 – 1.17 – 1.41 eV
The maximum velocity of photo electrons ejected is given as 1/2 m 
= 1.41 eV
or V max = 
= 7.036 × 10
5 m/sec
The radius of the circle traversed by photo electrons in magnetic field B is given by
r = 
= 
= 40.0 × 10 –3 meter (as qVB = 
) = 4.0 cm.
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