Showing posts with label Modern Physics. Show all posts
Showing posts with label Modern Physics. Show all posts

## Value of Half-Life Period

From the law of radioactive disintegration, we know,

## The Law of Radioactivity Disintegration:

Let, N be the number of atoms present in the radio element at a given instant t. Then the rate of decrease,

Here, λ is the disintegration constant. It is defined as the ratio of the amount of the substance which disintegrates in a unit time to the amount of substance present.

## General Properties of Nucleus:

### (i) Nuclear Size:

From Rutherford’s work, the mean radius of nucleus is  and the radius of the atom is . Thus the radius of the nucleus is 10,000 times smaller than the radius of the atom.

The empirical formula for the nuclear radius is,

Here, A is the mass number,  is a constant.

From this formula the radius of the Carbon () nucleus is.

## The Required de Broglie Wavelength:

A photon of light of frequency  has the momentum,

But, . Therefore, the momentum of the photon can be expressed in terms of wavelength λ as,

The wavelength of a photon is, therefore, specified by its momentum according to the relation,

## Einstein’s Photoelectric Equation :

According to Einstein, light of frequency  consists of a shower of photons, is of energy . When a photon of light of frequency  is incident on a metal, a part of the energy acquired by the electron is used to pull out the electron from the surface of the metal and the rest of it is utilized in imparting K.E. to the emitted electron.