## Limitations of Bohr's Model

Although Bohr's model of hydrogen atom and hyarogen like atom was successful in explaining the stability and spectrum even then it has few limitations. which are as follows:

(1) This model could not explain the spectrum of atom having more than one electron.

(2) This model could not explain the relative intensity of spectral lines. (i. e., few transitions are more acceptable than others why?)

(3) When a spectral line is observed by spectroscope of high resolution power, more than one lines are observed. This is known as fine structure of spectral line. Bohr model could not explain this.

(4) Splitting of spectral lines in external magnetic field (Zeeman's effect) and in external electric field (Stark's effect) could not be explained by this model.

(5) This model could not explain the distribution of electrons in different orbit.

Few limitations of Bohr's model are removed in Somer-field's model of atom. (In this model, the orbit of electron was considered as elliptical instead of circular ). But this model also has its limitations. Vector atomic model, which is based on quantum mechanics, explains clearly the structure of atom.

## Comparison of Isothermal and Adiabatic Processes for an Ideal Gas

Isothermal Process:

1.) In this process temperature remains constant i.e.$(\Delta T= 0)$.

2.) In this process internal energy remains constant i.e. $(\Delta U= 0)$.

3.) This process takes place very slowly.

4.) In this process the system is surrounded by a perfectly conducting material, whose conductivity is infinite.

5.) This process obeys Boyle's law i.e. $(PV= constant)$.

6.) In this process the slope of isothermal curve $=-\frac{P}{V}$

7.) In this process specific heat of gas should be infinite.

1.) In this process exchange of heat does not take place i.e. $(\Delta Q= 0)$ but temperature changes.

2.) In this process internal energy changes.

3.) This process takes place very rapidly.

4.) In this process the system is surrounded by a perfectly insulating material, whose conductivity is zero.

5.) This process obeys Poisson's law i.e. $(PV^{\gamma} = constant)$.

6.) In this process the slope of adiabatic curve $=- \gamma \frac{P}{V}$

7.) In this process specific heat of gas should be zero.

## Concept of Perfect Gas

Concept of Perfect (ideal) Gas:
An imaginary gas whose properties are similar to the properties of a real gas (a gas whose molecules occupy space and interact with each other) at infinitely low pressure. This imaginary gas is called 'perfect gas' or ideal gas'.
According to the definition, the following properties are imagined in a perfect gas :

(1) It strictly obeys Boyle's law, Charles' law, and the law of pressure under all conditions of temperature and pressure.

(2) Its pressure coefficient and volume coefficient are exactly equal to each other.

(2) Its molecules are infinitesimally small.

(3) There is no force of attraction between its molecules. Obviously, a perfect gas cannot be converted into a liquid or solid state, because a force of attraction is necessary between the molecules in the liquid or the solid state.

In practice, the gases that are difficult to liquefy, such as oxygen, nitrogen, hydrogen, and helium can be considered as perfect, although these are also not ideally perfect.

## Failure of Wave Theory in Explaining Photoelectric Emission Effect

Description of failure of wave theory in explaining photoelectric effect:

Although reflection, refraction, interference, diffraction and polarisation etc. are explained on the basis of wave theory but the laws of photoelectric effect cannot be explained on the basis of the wave theory of light. There are three main reasons for failure:

1.) According to wave theory, as the intensity of incident light increases, incident energy also increases. Therefore, greater is the intensity, greater will be the energy absorbed by the electrons of metal and therefore greater should be the kinetic energy of photoelectrons. From experimental observations, it is clear that the maximum kinetic energy of photoelectrons does not depend on the intensity of incident light.

2.) According to wave theory, photoelectric emission should occur for all the frequencies provided that it has enough energy to emit the electrons from the metal. Although from experimental observation it is clear that if the frequency of incident light is less than the threshold frequency, photoelectrons are not emitted.

3.) The energy carried by the light waves is absorbed by all the electrons and not by a single electron. Therefore, if the intensity of light is less, for the emission of electrons, there should be some time to collect sufficient energy. Although it is clear from experimental observation, the electrons are emitted instantaneously, whatever small be the intensity of light.