A monochromatic light is incident on a metallic plate having work function 
. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point 
. The distance between 
and 
is: (Given: The magnitude of charge of an electron is e and mass is m, h is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)
Text Solution
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To determine the distance between points 
and 
(where the electron re-enters the metallic plate), we first need to understand the electron's behavior in a magnetic field.
Maximum Kinetic Energy (KE): The energy of the emitted electron can be given by the photoelectric equation:
Here, 
is the energy of the incident photons, and 
is the work function of the metal.
Momentum (p): The momentum of the electron is related to its kinetic energy by the equation:
Path of Electron in Magnetic Field: When an electron moves perpendicularly through a magnetic field, it follows a circular path. The radius 
of this path is given by:
where 
is the charge of the electron, and 
is the magnetic field strength.
Distance Between 
and 
: Since the electron travels back to the plate, forming a complete semicircle, the distance between points 
and 
is twice the radius of this circular path:
Substituting the expression for momentum, we find:
Therefore, the distance between 
and 
is 
.
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