Nootan Solutions Matter Waves ISC Class-12 Physics Ch-24

Nootan Solutions Matter Waves ISC Class-12 Physics Ch-24 Nageen Prakashan Numericals. Step by step Solutions of Kumar and Mittal ISC Physics Class-12 Nageen Prakashan Numericals Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Physics.

Nootan Solutions Matter Waves ISC Class-12 Physics Ch-24

Board	ISC
Class	12
Subject	Physics
Publication	Nageen Prakashan
Writer	Kumar and Mittal
Vol	2nd
Book Name	Nootan
Chapter-24	Matter Waves
Topics	Solution of Numericals Questions
Page-Number	907, 908

Nootan Solutions Matter Waves ISC Class-12 Physics Ch-24

Wave Nature of Matter :-

The wave nature of matter is one of the most counter-intuitive concepts in Physics. You have seen examples of both particle nature of light and wave nature of light. You know about the Photoelectric effect due to Albert Einstein’s courtesy.

In the photoelectric effect, the electrons and photons exhibit the properties of a particle, just like a billiard ball. But you surely remember the Diffraction experiment and the Interference Rings.

Just like how two ripples on the surface of a pond interact. We see the wave nature of light in these cases. It’s an amazing mystery. It even involves our sight! The gathering and focusing mechanism of light by the eye-lens conform to the wave nature of light. But its absorption by the rods and cones of the retina conforms to the particle nature of light! While we were still struggling to understand this mystery, along came Louis de Broglie to make it even more complicated with his de Broglie Relation.

Heisenberg’s Uncertainty Principle :-

The Uncertainty Principle states that the momentum and position of a particle cannot be measured with precision simultaneously. In fact, there is always some uncertainty Δx in position and Δp in momentum. The uncertainties are related by,

Δx Δp ≤ h/2

If the momentum of a particle is measured accurately (i.e. p=0), the uncertainty x in its position becomes infinite. A particle with a definite momentum should have a definite wavelength, according to de Broglie’s equation. Such a wave should extend to infinity, which is unphysical. Any particle should be represented by a localized wave (wave packet), which consists of multiple wavelengths.

De Broglie’s Hypothesis :-

According to the hypothesis, particles behave as waves which are called matter waves. The wavelength (De Broglie wavelength) of the matter-wave corresponding to a particle of momentum p is given by,

λ=h/p

Here, h denotes the Planck’s constant. The De Broglie wavelength is inversely proportional to the momentum (hence mass) of a particle. For macroscopic objects, the wavelength is much smaller than the size of the object. The wave nature becomes prominent for microscopic objects e.g. electrons.

A photon having energy E has momentum:

p=E/c

Here, c denotes the speed of light in vacuum.

According to Planck’s concept, the energy of a photon of frequency and wavelength is given by,

E = hν = hc/λ

The energies should be equal, suggesting:

hc/λ = pc

λ=h/p

De Broglie realized that the above relation should hold for particles also. A particle of mass m and velocity v has momentum p=mv. Therefore, it should have a wavelength given by,

λ = h/p = h/mv

Nootan Numerical Solutions Matter Waves ISC Class-12 Physics Ch-24