Question

Describe dual nature of matter? Write de Broglie wavelength and frequency? Explain the electron microscope?

Write Bohr’s theory and assumptions for hydrogen atom with energy level diagram? Write Bohr’s correspondence principle?

Answer 1

1. Dual nature of matter - In case of light some phenomenon like diffraction and interference can be explained on the basis of its wave character. However, the certain other phenomenon such as black body radiation and photoelectric effect can be explained only on the basis of its particle nature. Thus, light is said to have a dual character.

Similarly in case of subatomic particle, few phenomena were not explained with the help of particle nature so these partucles like electrons seemed to be showing wave nature.

The relationship between momentum and wavelength for matter waves is given by p = h/λ, and the relationship energy and frequency is E = hf. The wavelength λ = h/p is called the de Broglie wavelength, and the relations λ = h/p and f = E/h are called the de Broglie relations.

 E(Energy) = hv = mc2

But v = c/λ

h c/λ   = mc2

(or) λ = h /mc

Electron Microscope :

An EM is a microscope that focuses beams of energetic electrons to examine objects up to nano-scales.

They utilize the same principles behind an optical microscope, but rather than photons or particles of light, concentrate electrons, charged particles located on the outside of atoms, onto an object. Electron microscopes use shaped magnetic fields to form electron optical lens systems that are analogous to the glass lenses of an optical light microscope.It is used in biomedical research to investigate the detailed structure of tissues, cells, organelles and macromolecular complexes. The high resolution of EM images results from the use of electrons as the source of illuminating radiation.

2.

• Bohr's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells, or orbits, around the nucleus.

• Bohr's model calculated the following energies for an electron in the shell, n.

• 

• the correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by the old quantum theory) reproduces classical physics in the limit of large quantum numbers. In other words, it says that for large orbits and for large energies, quantum calculations must agree with classical calculations. It says that the prediction of the quantum theory for the behaviour of any physical system must correspond to the prediction of classical physics in the limit in which the quantum numberspecifying the state of system becomes very large.

• Quantum theory = classical theory.