IIT JEE / CET – Main / Advanced Physics 2013 & 2014 Free Notes : Modern Physics > Photo electric effect

M O D E R N   P H Y S I C S

Modern physics , in essence refers to the post-Newtonian developments / studies in Physics. It incorporates elements of quantum mechanics and Einsteinian relativity. Modern physics often involves extreme conditions; quantum effects usually involve distances comparable to atoms ( nanometers ), while relativistic effects usually involve velocities comparable to the speed of light.

Unlike classical physics ,Modern physics is usually concerned with high velocities and small distances.

The inevitability of Modern physics – for eg , when analyzing the behavior of a gas at room temperature , most phenomena can be dealt with by the (classical) Maxwell –  Boltzmann distribution. But at or near absolute zero, the Maxwell–Boltzmann distribution fails to account for the observed behaviour of the gas, and hence the (modern) Fermi – Dirac or Bose – Einstein distributions have to be used instead. Similarly , photo-electric effect needed quantum theory to offer an explanation, which couldn’t be explained by Maxwell’s electromagnetic theory of light. Also, classical physics  (Rayleigh-Jeans law)  failed to account for black body radiation and later was explained by Planck’s law.

Photoelectric effect

Def – phenomenon in which charged particles  ( electrons / ions ) are released from a material ( usually metals ) when it absorbs electromagnetic / radiant energy. It can also occur if the radiation is in the wavelength range of ultraviolet radiation, X rays, or gamma rays. The emitting surface may be a solid, liquid or gas .The effect was discovered in 1887 by Heinrich Hertz and later explained by Albert Einstein .

According to the quantum theory proposed by Einstein in 1905 , electromagnetic radiation / light is quantized and exists in elementary numbers or quanta , called photons.The quantum of light wave of frequency f has the energy , E = hf , h is the Planck’s constant (6.63 × 10-34 m2 kg / s ). Light from any source is an integral multiple of quanta. Thus , Q = NE .  (where N is the no of photons , N = 1,2,3… ).

Now, E = hf  =  hc/λ   and  hc = 12400 eV.       Thus,  E = 12400/λ  in eV.

General properties > photons

  1. They travel in straight lines with the speed of light.
  2. They are not point masses , they are packets of energy.
  3. Their energy depends on their frequency.
  4. Energy is independent of the change in medium.
  5. A change of medium , changes their speed and wavelength , but not their frequency.
  6. As they are electrically neutral , they are not deflected by electric or magnetic feilds.
  7. They does not exist at rest as their rest mass is zero.
  8. They can show diffraction.
  9. They have momentum given by  P = h/λ .
  10. More intensity of light = more no of photons.

Emission of Photons / second

Consider a source of light ( energy ) emitting  light of wavelength λ  , having a power output of P watts. Then , the energy of each photon emitted by the source is  E = hv = hc/λ  . If the emitting source is 100 % efficient , then the no of photons emitted / second  – ( It is cosidered that the source  emitts photons uniformly in all directions )

n =  power of the source/ energy of a photon  = P/E  = Pλ / hc

Measuring Intensity of Light

Intensity of light basically measures the no of photons emitted / second in a particular direction. It could be generally defined as the radiant energy crossing / unit area perpendicular to the direction of it’s propagation. Consider a source emitting a cylindrical light beam of cross-sectional area A. If the power of the source is P , it’s intensity is given by –     I = P/A W/m² .

Suppose the source is pointed and isotropic , then          I = P/4 π r² W/m² . ( here we consider a circular area around the light source and r is the radius of this circle . Naturally , we consider that the source emits radiation  uniformly in all directions )

Inverse square law of Light –   This law states that the intensity of light observed from a source of constant intrinsic luminosity falls off as the square of the distance from the object. ( intrinsic here means the light is produced by the source through it’s own process )

Photon  Flux

Photon flux image - intensity / distance of radiation source.

Defined as the number of photons incident on a normal surface / second / unit area .

If a light beam of intensity I W / m²  , having wavelength λ  is incident on a surface , then it’s photon flux is  –

Φ   =  Intensity / Energy of a photon   =  I / ( hc / λ )  =  I λ  / hc  .

Now , consider a point source of uniform radiation of power P watts. The photons emitted / second are –

n =  Power of the source / Energy of a photon   =  P  /  ( hc / λ )   =  P λ / hc .

The emitted photons fill a spherical space around the point source of radiation . Consequently , the photon flux at a distance r from the point source is given by   –

Φ = No of photons emitted /second / surface area of the spherical space of radius r = n / 4 π r²   .

(  to continue ……….. )

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