Module 1 : Quantum Mechanics
Chapter 2 : Introduction to Quantum ideas
 
  Introduction to Quantum ideas  
  where $\nu$ is the frequency of the incident radiation and $\nu_0$ is the critical frequency below which no electrons are emitted.
(3) The electrons are emitted almost instantaneously without any noticeable time delay.
These observations are not consistent with wave description of e.m. radiation. The results suggest 		 
 
$\displaystyle eV_0$ $\textstyle =$ $\displaystyle h(\nu-\nu_0),\qquad h=6.625\times 10^{-34} JS,$
 
 
$\displaystyle \frac{1}{2}mv_m^2$ $\textstyle =$ $\displaystyle h\nu-e\phi,\qquad h\nu_0=e\phi,$
(2.3)
  where the observed proportionality constant $h$ is Planck's constant. Einstein's interpretation (1905) was that radiation comes in energy quanta $h\nu$, photons, and their energy goes into overcoming the minimum binding energy $e\phi$ called the work function, and into the kinetic energy of the emitted electrons. Some important points to be noted are:
(1) Ultraviolet radiation is needed since $h\nu=e\phi$ and $e\phi$ is of the order of 3-5 eV for alkali metals. The value of $h\nu$ for visible radiation is about 2.5 eV.
(2) Alkali metal plates are needed since they have the lowest work functions, 3-5 eV.
(3) Only a small fraction of incident radiation, 5 percent is responsible for ejecting electrons, the rest is absorbed by the plate as a whole.
(4) Photoelectric effect in atoms in the form of gases, is described as photo-ionization. Here since there is no collective absorption, number of photons absorbed is equal to the number of electrons ejected.
(5)Energy for emission can come from heating, thermionic emission. In this case the rate of emission is determined by statistical properties in terms of $e\phi$ and temperature T.
(6) With the development of very high intensity radiation in the form of lasers, now we can have multi-photon absorption for which one has the relation
  \begin{displaymath} nh\nu-e\phi=\frac{1}{2}mv_m^2 \end{displaymath} (2.4)
  for energy conservation, where $n$ is the number of photons absorbed by a single electron.