Waves and its Characteristics
It is a periodical disturbance causing the transfer of energy without the transfer of matter.
➢ Characteristics of Waves
- Amplitude: Maximum displacement from the mean position it remains constant with distance except for stationary or standing waves.
- Wavelength: It is the distance between two adjacent crest or troughs.
- Frequency (m or n): The no of waves passing through a point in 1 second, unit-sec-1 or Hz.
- Wavenumber: No. of waves present in the unit distance. etc.
- Velocity: linear distance travelled by wave in one second.
Question 1:The frequency of a wave is 6 × 1015 s–1. Its wave number would be
- Whenever a charge is placed in an electric or a magnetic field, it experiences a certain force acting on it or if multiple charges are placed, they experience an interaction due to another.
- In the year 1870, James Maxwell became the first scientist to explain the interaction between the charges in the presence of the electric and magnetic fields.
He proposed that when electrically charged particles perform an accelerating motion, alternating electrical and magnetic fields are produced and transmitted. These fields traverse in the forms of waves known as electromagnetic radiation. A light wave is an example of electromagnetic radiation.
➢ Maxwell Electromagnetic Wave Theory (Wave Nature of Light)
- An accelerated electrically charged particle produces and transmits an electrical and magnetic field. These are transmitted in the form of waves known as electromagnetic waves or electromagnetic radiations.
- He stated that light also possesses an electrical and magnetic field, and it is also known as electromagnetic radiations or e.m.w.
➢ Properties of Electromagnetic Radiation
- The oscillating charged particles produce oscillating electric and magnetic fields which are perpendicular to each other and both are perpendicular to the direction of propagation of the wave.
- Electromagnetic waves do not require a medium i.e., they can travel in a vacuum too.
- The velocity of all electromagnetic radiations is 3 × 108 m/s in a vacuum.
- The energy of an electromagnetic wave is directly proportional to the intensity, and it is independent of frequency.
- There are many kinds of electromagnetic radiation, differing from one another in terms of wavelength or frequency. This electromagnetic radiation as a whole constitutes the electromagnetic spectrum.
Example: Radiofrequency region, microwave region, infrared region, ultraviolet region, visible region etc.
- Electromagnetic radiation is characterized based on various properties like frequency, wavelength, time period etc.
- Electromagnetic Radiation also shows diffraction and interference and therefore, Maxwell concluded light to be wave nature.
- But Maxwell theory couldn't explain the results of the Photoelectric Effect and Black Body Radiations.
➢ Electromagnetic Radiation Formula
- Frequency is defined as the number of waves that pass through a given point in one second. Mathematically it is equal to the reciprocal of the time period of electromagnetic radiation.
- A general equation relating the speed of light, frequency, and wavelength of electromagnetic radiation is given below,
c = ν l
c = speed of light
ν = frequency of the electromagnetic wave
l = wavelength of the electromagnetic wave
- Apart from frequency and wavelength, some other parameters are also used to categorize electromagnetic radiation. One of these parameters is the wavenumber.
- Wavenumber is defined as the number of wavelengths per unit length. Mathematically, it is equal to the reciprocal of the wavelength. It is expressed in the SI unit as m.
➢ Photon Energies for EM SpectrumEM Spectrum
- A black body is an object that emits a well-defined spectrum of radiation solely based on its temperature. We see from the figure at right that the hotter the black body, the more intense it is, and the shorter the peak wavelength.
- The picture does not say anything about what the object is made of, or how heavy it is, etc. It doesn't matter! The only property that determines the spectrum of a black body is its temperature.
- Brick, iron or a dense gas will emit the same spectrum as long as they are at the same temperature. That spectrum will have a peak that lies at a particular wavelength.
Graph of Intensity vs Wavelength
Particle Nature of Light
➢ Planck's Quantum Theory
- He stated that a body radiates energy in the form of discontinuous energy packets or bundles. Each bundle of energy is known as quantum, and the quantum of light is known as photons. The energy of each quantum is directly proportional to the frequency of radiation.
E = hv
h = 6.62 × 10-34 Js.
➢ Plank's Constant
- Total energy absorbed or emitted by a body will be whole no. integral multiple of the energy of quantum. i.e., Eabs or Eemitted = nhν.
- Exercise. Calculate the no. of photons emitted by the 60-watt bulb in 10 hrs. When the light of wavelength 6000 Å is emitted by it.
Sol. = 6.5 × 1024 J
Question 2:The number of photons of light of wavelength 7000 Å equivalent to 1 J are
Question 3:Which is not characteristic of Planck’s quantum theory of radiation?
➢ Energies in Electron Volts
- Room temperature thermal energy of a molecule = 0.04 eV
- Visible light photons = 1.5-3.5 eV
- Energy for the dissociation of an NaCl molecule into Na and Cl- ions: = 4.2 eV
- Ionization energy of atomic hydrogen = 13.6 eV
- Approximate energy of an electron striking a color television screen (CRT display) = 20,000 eV
- High energy diagnostic medical x-ray photons.= 200,000 eV (=0.2 MeV)
Typical Energies From Nuclear Decay:
- gamma = 0-3 MeV
- beta = 0-3 MeV
- alpha = 2-10 MeV
- Cosmic ray energies = 1 MeV - 1000 TeV
- 1 MeV = 106 eV, 1 GeV = 109 eV, 1 TeV = 1012 eV.
➢ Explanation of Black Body Radiations Using Planck's Quantum Theory
- When a solid substance like the iron piece is heated, it emits radiations. As heating is continued, more and more energy is being absorbed by the atom, and hence, more energy will be emitted and therefore the energy of e.m.w. increases and frequency of e.m.w. increases and therefore, body first becomes red then yellow and finally white.
- Therefore, it can be concluded that light posses particle nature and energy of electromagnetic radiation depends upon frequency.
➢ Explanation of Photoelectric Effect Using Planck's Quantum Theory
- When a metal sheet is subjected to electromagnetic radiation of suitable frequency then some electrons are ejected from the metal surface, and these electrons are known as photoelectron, and the effect is known as the photoelectric effect.
- If electromagnetic radiation of low frequency is used, then there is no ejection of electron despite the continuous increasing intensity. This observation was contradicting to Maxwell theory according to which energy electromagnetic radiation ∝ I but can be explained using Planck's quantum theory, i.e. E ∝ ν.
➢ Dual Nature of Light
- Since the wave nature of light explains the diffraction interference phenomenon while particle nature explains black body radiation and photoelectric effect light was considered to have dual nature particle nature as well as wave nature.Dual Nature of Light
Emission & Absorption Spectrum
Spectra can be divided into two types based on absorption by gas or vapour & white light emission:
1. Emission Spectrum: Spectrum due to the emission of white light by gas at high temperature is known as an emission spectrum. This kind of spectrum usually consists of bright lines on the dark background. The emission of energy by electrons generates an emission spectrum.
2. Absorption Spectrum: The spectrum which occurs due to absorption of white light by gas and transmitted white light, it is termed as an absorption spectrum. Unlike the emission spectrum, it consists of dark lines on the bright background. it is due to the absorption of energy by electrons.
Spectra can be divided into two types depending on the spectral lines:
- Line Spectrum or Atomic Spectrum: This is made up of distinct lines. When an electron in an atom excites and de-excites, this spectrum occurs. Emission & absorption spectra show the line spectrum.
- Band Spectrum: It is a characteristic of a molecule. It consists of closely spaced lines called bands. In a molecule, the vibration & rotation of atoms generates such a spectrum.
Emission of an electron from the metal surface when the light of suitable frequency is subjected to the metal surface. The effect is known as the photoelectric effect and the ejected electrons are known as photoelectrons.
Fig: Photoelectric effect.➢ Terms Used in the Photoelectric Effect
1. Work function (w): It is the minimum amount of energy required to cause photoemission from the metal surface. It is also known as threshold energy or Binding energy. [Work function depends upon ionization energy and therefore w is minimum for alkali metals].
2. Threshold frequency (n0): The minimum value of frequency that can cause photoemissions. If n < n0, then there is no photoemission.
w = h n0 ⇒
3. Threshold wavelength (l0): The maximum value of wavelength that can cause photoemission.
If l > l0, then photoemission is not possible.
4. Intensity (I): Energy falling on the metal surface of unit area of unit time
5. Photo intensity (IP): It is the number of photons falling per unit area per unit time.
Relation between I and Ip: I = Ip hn
Photo intensity is independent of frequency while intensity depends on frequency.
6. Power: Total energy radiated per unit time.
➢ Effect of Variation of frequency
- Effect of Photon Emission: I = Iphn
If the frequency of subjected photon increases (intensity increases keeping photo intensity constant) then there is no change in the number of ejected photoelectrons as well as no change in photocurrent.
- Effect on kinetic Energy: Average k. E. as well as K.E.max increases with an increase in frequency.
hn - W = K Emax.
K Emax = hn - hn0 (y = mx + c)
K Emax = hn -
KEmax = hn - w
- Effect of Variation of Photo Intensity: On increasing intensity, keeping the frequency constant (i.e. increasing photo intensity) no of ejected photoelectrons increases as well as photocurrent increases.Graph of photocurrent vs voltage.
- Effect on Kinetic Energy: Average K.E. and K.Emax remain constant with change in photo intensity.
➢ Stopping Potential or Retarding Potential (V0)
It is the minimum potential required to stop the fastest moving electrons completely or it is the minimum potential at which photocurrent becomes zero.
eV0 = hn - w
eV0 = hn - hn0
It can be commented that stopping potential increase with the increase in frequency however if photo intensity is changed there is no effect on stopping potential.
Graph of Photocurrent vs cell voltage.
Exercise: In ultraviolet light of wavelength 200 nm is used in an experiment of photoelectric effect with lithium cathode (w = 2.5 eV). Then calculate
(i) K.Emax (ii) Stopping potential
Sol. K.Emax = hn - w
⇒ 6.2 - 2.5
⇒ 3.7 eV
Stopping Potential = 3.7 V