### Value of Half-Life Period

From the law of radioactive disintegration, we know,

If,  be the half life period, then at,

### 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.

### Electric Flux

For an arbitrary closed surface, the net outward flow or flux is the product of the average outdrawn normal component of the vector and the area of surface. Electric flux is used to express the relation between  and its source. Flux is denoted by

= (average normal component)×(surface area)

The unit of electric flux is newton-meter2/coul.

### Flux

If  is a vector field, then the flux through any face is defined as the scalar product of the vector area of the face and the vector . That is,

Flux = (component of velocity normal to the face) × (area of the face)

The amount of flux per unit area is defined as the divergence of the vector

### Electric Charge

The reason present in a material causes static electricity, electric field in the material and the material become able to attract other materials is called electric charge. It may be positive or negative. Unit of electric charge is coulomb (C).

### What are dextrorotatory and laevorotatory substances?

Dextrorotatory and laevorotatory substances are optically active substances.

#### Dextrorotatory  substances

Substances which rotate the plane of polarization of the light towards the right are known as dextrorotatory substances.

#### Laevorotatory substances

Substances which rotate the plane of polarization of the light towards the left are known as laevorotatory substances.

### Optical activity

Optical activity is the ability of a substance to rotate the plane of polarization of plane polarized light. Substances which have this ability are called optically active substance. Tartaric acid is an example of optically active liquid.

### Nicol prism

Nicol prism was invented by William Nicol in 1828. It is an optical device used for producing and analyzing plane polarized light. The nicol prism is made in such a way that it eliminates one of the two rays by total internal reflection. It is generally found that it eliminates the ordinary ray and only the extraordinary ray is transmitted through the prism.

### Double refraction

Erasmus Bartholinus discovered in 1669, that, when a ray of light is refracted by a crystal of calcite it gives two refracted rays. This phenomenon is called double refraction. Calcite is crystallized calcium carbonate (CaCO3). It crystallizes in many forms and can be reduced by cleavage or breakage into a rhombohedra.

### Phase velocity

Phase velocity is the velocity with which a plane progressive wave front travels forward. Phase velocity is symbolized by . It has a constant phase =

### Group velocity

The group velocity () is the speed with which the point of reinforcement of the resultant wave travels. The group velocity is different from the individual wave velocity.

### Phase angle

Phase angle is defines as the fraction of the time interval that has lapsed since the particle has crossed the mean position of rest in the positive direction. It is also equal to the angle swept by the radius vector since the vibrating particle last crossed its mean position of rest.