## Photo Electric effect

When light falls on metal some of the electrons are emitted from the surface of the metal. This phenomenon is termed as photo electric effect.

Photo electric effect

In 1905 Albert Einstein explained photo electric effect using the Planck’s hypothesis which states that the energy of light is quantized. Light consists of tiny mass less particles called photons. Photon is a quantum of electromagnetic energy which carry energy of h*v where h is Planck’s constant and v is frequency of light. The energy the impinging photons should be at least equal to work function .i.e.

W.f = h*vo

Where vo is the critical frequency. Below vo there exists no photo electron emissions. The Work function is the characteristic property of metal depending on atomic and lattice structure of that particular metal. Greater the work function of the metal, the more energy is needed for an electron to leave its surface and higher the critical frequency of photo emission to occur. If the impinging photon on metal is having energy greater than the work function of metal the extra energy will appear as kinetic energy of ejected electron. Accordingly we can write

h*v = W.f + K.E

Where W.f is the work function of metal, K.E is the kinetic energy of ejected electron. Consider the following apparatus with light falling on a metal which acts as cathode emitting electrons, a retarded potential can be applied between cathode and anode to estimate the velocity of electrons.

Photo electric apparatus

For zero Vr all the electrons ejected from the cathode will reach the anode. As the retarding potential increases the photo current decreases. It becomes almost zero for critical voltage known as stopping potential which is given as

(½)*me*V2 = e*Vs.p

where me is the mass of electron=9.1*10-31 kg,

V is the velocity of electron,

e is the charge of electron,

Vs.p is stopping potential.

The variation of stopping potential v/s frequency and the photo current v/s Intensity of incident light is plotted in the figure

Stopping potential v/s frequency

Photo current v/s intensity

From the plot is can be deduced that the kinetic energy of electrons increases as frequency of impinging photons increases.

Kinetic Energy = (½)*me*V2

h*(v- vo) = (½)*me*V2

Hence the velocity of ejected electrons =√(2*h*(v- vo)/me). Hence as the frequency increases the photo current (number of electrons ejected from the metal per unit time) remains the same but the velocity of ejected electrons increases.  But as the intensity of incident light increases the photo current increases but the velocity of ejected electrons remains constant.

Intensity is defined as the incident light energy per unit area per unit time. Hence as the intensity increases the number of photons impinging on the metal increases hence the number of electrons ejected from the metal per unit time increases.

## Photo ionization

When light falls on an atom it will eject one or more electrons (depending on energy of photons) from it forming ions. This process is called Photo ionization. Photo ionization and photo electric effects are one and same process which essentially involves interaction of matter with electromagnetic radiation. The term Photo ionization is used with regard to isolated or non interacting atoms whereas photo electric effect is used with regard to metals. The photo ionizationof helium atom is ahown in the figure. The ionization energy of helium atom for removing first electron = 54.4 eV.

Photo ionization