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.
Adiabatic Process:
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:
(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.
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 :
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.
Einstein Photoelectric Emission Effect Law
Description of the Light:
According to the Albert Einstein
Theory of Photoelectric Effect:
When the photon of ultraviolet ray is incident on the metal then this energy is used in two parts:
1.) To emit the electron from a metal surface i.e. Work Function. The electron emitted from a metal surface is called the photoelectron.
2.) Remaining energy increases the kinetic energy of the emitted photoelectron. This is the maximum kinetic energy of the photoelectron.
Let us consider
The energy of incident Ultraviolet Photon $E=h\nu$
The work function $W= h \nu_{\circ}$
The maximum kinetic energy of photo electron $K_{max}= \frac{1}{2}mv^{2}_{max}$
According to Einstein's photoelectric effect theory
$E=W+K_{max}$
$h \nu = h \nu_{\circ} + \frac{1}{2}m v^{2}_{max}$
$h \nu - h \nu_{\circ} = \frac{1}{2}m v^{2}_{max}$
$h \left( \nu - \nu_{\circ} \right) = \frac{1}{2}m v^{2}_{max}$
Where
$\nu \rightarrow$ Frequency of incident Ultraviolet ray photon
$\nu_{\circ} \rightarrow$ Threshold frequency to emit the photoelectron from the metal surface
$ v_{max} \rightarrow$ Maximum velocity of emitted photoelectron from the metal surface
The light is consist of small packets or bundles of energy. These packets are called photon. The energy of each photon is $h \nu$.
$\nu \rightarrow$ Frequency of incident Ultraviolet ray photon
$\nu_{\circ} \rightarrow$ Threshold frequency to emit the photoelectron from the metal surface
$ v_{max} \rightarrow$ Maximum velocity of emitted photoelectron from the metal surface
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