# Atomic Structure

## Black Body Radiation

When a body is heated, it emits electromagnetic radiation and when temperature is dropped, the energy is absorbed by the body. If a body absorbs all radiations that falls upon it, it is called the**Black Body**and the radiation emitted by it is called

**Black Body Radiation**

No any object is perfectly black body.

In 1854, Kirchoff proposed the following two laws concerning black body. They are-

1. A black body not only absorbs all radiation falls upon it but also acts as a perfect radiator when heated.

2. The radiation given out by a black body depends upon the temperature of body and is not dependent on the nature of the interior materials.

## Plank's Quantum Theory

This theory explains the spectral distribution of black body radiation. i.e. how the energy distributed among different wavelengths emitted by a black body.Followings are the main points of this theory-

1. Energy emitted or absorbed is not continuous, but is in the form of packets called quanta. Quanta may be taken as behaving like a strem of particles having mass, energy and momentum. The energy of quantum radiation is-

E = hν (where 'h' is Plank's Constant & 'ν' is frequency of radiation)

or, E ∝ ν

2. Each photon carries an energy in discrete level which is directly proportional to the frequency of wavelength. The energy of the nth enenrgy level is given as-

E = nhν

where 'n' is integer having values 0,1,2,3...

## Compton Effect

When x-rays fall on a crystal, they are scatterd. Compton in 1923, observed that the wave length of the scattered radiation(λ^{'}) is always greater that the wavelength of the incident radiation(λ)

i.e. λ

^{'}> λ

The change in wavelength is independent of the wavelength of the incident radiation as well as that of scatterer. The change in wavelength of the scattered radiation is called

**Compton effect**.

## de-Broglie Wave Equation

The de Broglie equation is used to describe the wave properties of matter, specifically, the wave nature of the electron.de Broglie equation states that a matter can act as waves and particles like light and radiation.

We know that Einstein's equation-

E = mc

^{2}---------(eq.1)

where, E = energy, m = mass the particles and c is the velocity of light

According to Plank's rdiation theory-

E = hν = h.c/λ ---------(eq.2)

where, h = Plank's constant and λ = wave length of radiation

From equation 1 and 2 we have-

mc

^{2}= h.c/λ

or, mc = h/λ

or, p = h/λ [as mass(m) X velocity(c) = momentum(p)]

or,

**λ = h/p**---------(eq.3)

Equation '3' is called de-Broglie Wave Equation.

Question: Find the de Broglie wavelength for an electron moving at the speed of 5.0×10^{6}m/s (mass of an electron is 9.1×10^{−31}kg )

[Hints: λ = h/mv

h = 6.63×10^{−34}J⋅s]

Answer: 1.46×10^{−10}m

## Heisenberg Uncertainty Principle

It is not possible to determine precisely and simultaneously the momentum and position of small moving particles.If position of te particle is known then momentum is unknown and vice-versa.

Δx. Δp ≥ ℏ/2 = h/4π

where, Δx = uncertain position, Δp = uncertain momentum, ℏ = h/2π & h = Plank's constant

Δx. mΔv ≥ ℏ/2

Δx. Δv ≥ ℏ/2m

Δx. Δv ≥ h/4πm

Question: A particle is moving with constant momentum. The uncertainty in the momentum of the particle is 3.3 x 10

[Hints: Δx = ℏ/2.Δp

Δx = 5.27 ☓ 10

1.59 ☓ 10

^{-2}kg ms^{-1}. Calculate the uncertainty position.[Hints: Δx = ℏ/2.Δp

Δx = 5.27 ☓ 10

^{-35}/3.3 ☓ 10^{-2}1.59 ☓ 10

^{-33}m]