# 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 :-**

**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

**Nageen Prakashan Numericals**

Question 1:

What is de-Broglie wavelength of a 2 kg object moving at speed of 1 ms^{ -1 ?}

Question 2:

Calculate ……………….. kg ms^{ -1 }

Question 3:

……………………..

……………………..

……………………..

Question 9:

Calculate de-Broglie ………………. energy 400 eV.

Question 10:

What potential must be applied to an electron microscope to produce electrons of wavelength 1.0 Å ?

—: End of **Nootan Solutions Photoelectric Effect** :–

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