Module 5 : MODERN PHYSICS
Lecture 24 : Photoelectric Effect
  The electrons which are more tightly bound to the metal (e.g. electrons which lie two or three atomic layers below the surface) require more energy to be removed. We define Work Function $ \varphi$ of a metal as the minimu energy that must be supplied to an electron at the metal surface to dislodge it from the metal. Such electrons are emitted with maximum possible kinetic energy. Thus Einstein's equation becomes
 
$\displaystyle K_{max} = \frac{1}{2}mv_{max}^2 = h\nu -\varphi$
  Since kinetic energy cannot be negative, the above equation implies the existence of a minimum frequency $ \nu_{th}$ for photoemission to take place
 
$\displaystyle h\nu_{th} = \varphi \ \ \ {\rm i.e.} \nu_{th} = \frac{\varphi}{h}$
  Using this, we can reqrite rewrite Einstein's equation as
 
$\displaystyle K_{max} = h(\nu-\nu_{th})$
  To stop such maximum energy electrons from reaching the anode, we must apply a reverse potential $ V_s$, given by $ eV_s = K_{max}$. Thus
 
$\displaystyle eV_s = h\nu-\varphi$
 
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