** 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.*

* *

**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} m^{2} 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 –

- They travel in straight lines with the speed of light.
- They are not point masses , they are packets of energy.
- Their energy depends on their frequency.
- Energy is independent of the change in medium.
- A change of medium , changes their speed and wavelength , but not their frequency.
- As they are electrically neutral , they are not deflected by electric or magnetic feilds.
- They does not exist at rest as their rest mass is zero.
- They can show diffraction.
- They have momentum given by P = h/λ .
- 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** –

* *

*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 ……….. )