JEE Advanced
JEE Main
BITSAT
View complete IIT JEE section
NTSE
KVPY
Olympiads
CBSE
ISCE
UAE
Saudi Arabia
Qatar
Kuwait
Oman
Bahrain
View complete NRI section
Physics
Chemistry
Maths
Revision notes
View complete study material
Buy IIT JEE/AIPMT study material
Buy CBSE Grade 8/9/10 study material
Dual Nature of Matter and Photoelectric Effcet
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. Such studies on light were made by Einstein in 1905.
Louis de Broglie, in 1924 extended the idea of photons to material particles such as electron and he proposed that matter also has a dual character-as wave and as particle.
The wavelength of the wave associated with any material particle was calculated by analogy with photon.
In case of photon, if it is assumed to have wave character, its energy is given by
(According to the Planck’s quantum theory)
Where nth frequency of the wave and ‘h’ is is Planck’s constant
If the photon is supposed to have particle character, its energy is given by
E = mc2 … (ii)
(according to Einstein’s equation)
where ‘m’ is the mass of photon, ‘c’ is the velocity of light.
h c/λ = mc2
The above equation is applicable to material particle if the mass and velocity of photon is replaced by the mass and velocity of material particle. Thus for any material particle like electron.
λ = h/mv or λ = where mv = p is the momentum of the particle.
If the wave is completely in phase, the circumference of the orbit must be equal to an integral multiple of wave length (λ)
Therefore 2πr = nλ
where ‘n’ is an integer and ‘r’ is the radius of the orbit
∴ 2πr = nh /mv or mvr = n h/2π
“Thus, the number of waves an electron makes in a particular Bohr orbit in one complete revolution is equal to the principal quantum number of the orbit”.
Number of waves ‘n’ = 2πr / λ = 2πr / h/mv = 2πmvr / h
Where v and r are the velocity of electron and radius of that particular Bohr orbit in which number of waves are to be calculated, respectively.
The electron is revolving around the nucleus in a circular orbit. How many revolutions it can make in one second?
Let the velocity of electron be v m/sec. The distance it has to travel for one revolution 2πr, (i.e., the circumference of the circle).
Thus, the number of revolutions per second is = v / 2πr
Common unit of energy is electron volt which is amount of energy given when an electron is accelerated by a potential of exactly 1 volt. This energy equals the product of voltage and charge. Since in SI units coulombs x volts = joules, 1 eV numerically equals the electronic charge except that joule replaces coulombs.
When a black body is heated, it emits thermal radiations of different wavelengths or frequency. To explain these radiations, Max Planck put forward a theory known as Planck’s quantum theory. The main points of quantum theory are
Sir J.J. Thomson, observed that when a light of certain frequency strikes the surface of a metal, electrons are ejected from the metal. This phenomenon is known asphotoelectric effect and the ejected electrons are called photoelectrons.
A few metals, which are having low ionization energy like Cesium, show this effect under the action of visible light but many more show it under the action of more energetic ultraviolet light.
An evacuated tube contains two electrodes connected to a source of variable voltage, with the metal plate whose surface is irradiated as the anode. Some of the photoelectrons that emerge from this surface have enough energy to reach the cathode despite its negative polarity, and they constitute the measured current. The slower photoelectrons are repelled before they get to the cathode. When the voltage is increased to a certain value V_{0}, of the order of several volts, no more photoelectrons arrive, as indicated by the current dropping to zero. This extinction voltage (or also referred as stopping potential) corresponds to the maximum photoelectron kinetic energy i.e., eV_{o} = ½ mv^{2}
The experimental findings are summarized as below:
Light must have stream of energy particles or quanta of energy (hv). Suppose, the threshold frequency of light required to eject electrons from a metal is n_{0}, when a photon of light of this frequency strikes a metal it imparts its entire energy (hv_{0}) to the electron.
“This energy enables the electron to break away from the atom by overcoming the attractive influence of the nucleus”. Thus each photon can eject one electron. If the frequency of light is less than v_{0} there is no ejection of electron. If the frequency of light is higher than v_{0} (let it be v), the photon of this light having higher energy (hv), will impart some energy to the electron that is needed to remove it from the atom. The excess energy would give a certain velocity (i.e, kinetic energy) to the electron.
hv = hv_{0} + K.E
hv = hv_{0} + ½ mv^{2}
Where, v = frequency of the incident light
hv_{0} is the threshold energy (or) the work function denoted by Φ = hv_{0} (minimum energy of the photon to liberate electron). It is constant for particular metal and is also equal to the ionization potential of gaseous atoms.
The kinetic energy of the photoelectrons increases linearly with the frequency of incident light. Thus, if the energy of the ejected electrons is plotted as a function of frequency, it result in a straight line whose slope is equal to Planck’s constant ‘h’ and whose intercept is hn_{0}.
Click here to access the Organic Chemistry Revision Notes and IIT JEE Chemistry Syllabus
Problems with Solutions True and False Problem:...
Calculation of Velocity: We know that mvr =...
QUANTUM NUMBERS An atom contains large number of...
Atomic Models We know the fundamental particles of...
Quantum Mechanical Model of Atom...
Discovery of Electron, Proton & Neutron Lets...
FUNDAMENTAL PARTICLES Atoms are made...
Relation between Kinetic Energy and Wavelength:...
ATOMIC SPECTRUM If the atom gains energy the...
DISCOVERY OF PROTON: POSITIVE RAYS OR CANAL RAYS...
Wavelengths of Electromagnetic Radiations:...
ATOMIC TERM Nuclide: Various species of atoms in...
Hund’s Rule of Maximum Multiplicity: This...
Solved Questions of Atomic Structure Part I...
Radius and Energy Levels of Hydrogen Atom:...
Characteristics of Wave SOME IMPORTANT...
A-Scattering Experiment Conclusions of...
HEISENBERG’S UNCERTAINTY PRINCIPLE All...
BOHR’S ATOMIC MODEL Bohr developed a model...
Calculation of Energy of an Electron: The total...
HYDROGEN ATOM If an electric discharge is passed...
Objective Questions of Atomic Structure Problem:...
Derivation of Angular Momentum from de Broglie...
PLANCK’S QUANTUM THEORY When a black body is...
Electronic Configuration Rules for filling of...
Electromagnetic Radiations Some Important...
DISCOVERY OF NEUTRON After the discovery of...
Pauli’s Exclusion Principle: According to...
Merits of Bohr’s Theory: * The experimental...
PHOTOELECTRIC EFFECT Sir J.J. Thomson, observed...