Revision: Dual Nature of Radiation and Matter Physics HSC Science (General) 12th Standard Board Exam Maharashtra State Board

The minimum frequency of incident radiation required to start photoemission in any photosensitive material is known as the threshold frequency. 

The phenomenon of emission of electrons from a metal surface, when radiation of appropriate frequency is incident on it, is called the Photoelectric Effect.

The phenomenon of emission of electrons from a metal surface when radiation of appropriate frequency is incident on it is known as the photoelectric effect. 

A device that makes use of the photoelectric effect and converts light energy into electrical energy is called a Photocell.

The wave associated with a moving material particle of total energy E and momentum p is called a De-Broglie Wave or Matter Wave, and its wavelength is called the De-Broglie Wavelength.

The phenomenon in which material particles show wave-like nature under certain circumstances is called Wave-Particle Duality of Matter.

The minimum amount of energy required to be provided to an electron to pull it out of the metal from the surface is called the work function of the metal.

A surface that emits electrons when illuminated with suitable radiation is called a photosensitive surface.

When the anode is at positive potential with respect to the cathode, it accelerates the emitted electrons. This potential is called accelerating potential.

When the anode is at negative potential with respect to the cathode, it opposes the motion of electrons. This is called retarding potential.

The minimum negative potential applied to the collector to reduce the photocurrent to zero is called the stopping potential (cut-off potential).

The relation E = hν, which connects the energy of a photon with its frequency, is called Einstein’s relation.

The wavelength associated with a moving material particle is called the de Broglie wavelength.

The emission of electrons from a metal surface by heating it to high temperature is called thermionic emission.

The emission of electrons from a metal surface by applying a strong electric field is called field emission.

A microscope that uses accelerated electron beams instead of visible light to obtain high-resolution images is called an electron microscope.

A device that uses the photoelectric effect to convert light energy into electrical energy is called a photocell.

The quantum (bundle) of electromagnetic radiation having energy E = hν is called a photon.

The property of electromagnetic radiation to exhibit both wave nature and particle nature is called wave–particle duality of electromagnetic radiation.

The change in wavelength of X-rays after scattering from electrons is called the Compton shift.

The minimum frequency of incident radiation required to eject electrons from a metal surface (ν₀ = ϕ₀/h) is called the threshold frequency.

The maximum kinetic energy of emitted photoelectrons given by KE_max⁡ = hν − ϕ₀​ is called Einstein’s photoelectric equation.

The hypothesis that matter, like radiation, exhibits both wave and particle nature is called the de Broglie hypothesis.

The waves associated with moving material particles are called matter waves.

Electrons emitted from a metal surface due to incident light are called photoelectrons.

The phenomenon of emission of electrons from a metal surface when radiation of appropriate frequency is incident on it is called the photoelectric effect.

Electromagnetic radiation consists of mutually perpendicular oscillating electric and magnetic fields, both perpendicular to the direction of propagation of the wave.

The minimum energy required to remove an electron from the surface of a metal is called the work function of the metal.
It is denoted by ϕ₀.

De-Broglie Wavelength (general): \[\lambda=\frac{h}{p}=\frac{h}{mv}=\frac{h}{\sqrt{2mE}}\]

De-Broglie Wavelength (neutron): \[\lambda=\frac{h}{\sqrt{2mE}}=\frac{0.286}{\sqrt{V}}\mathrm{\r{A}}=\frac{1.23}{\sqrt{V}}\mathrm{nm}\]

De-Broglie Wavelength (gas molecule): \[\lambda=\frac{h}{m\times v_{rms}}\]

\[
e = 1.602 \times 10^{-19}\,\text{C}
\]

\[
1\,\text{eV} = 1.602 \times 10^{-19}\,\text{J}
\]

\[
\frac{e}{m} = 1.76 \times 10^{11}\,\text{C/kg}
\]

λ = \[\frac {h}{p}\]

\[
\lambda = \frac{h}{mv}
\]

\[
K_{\text{max}} = eV_0
\]

             or

\[
K_{\text{max}} = h\nu - \phi_0
\]

Linear Form:

\[
V_0 = \frac{h}{e}\nu - \frac{\phi_0}{e}
\]

\[
p = \frac{h\nu}{c} = \frac{h}{\lambda}
\]

\[\Delta\lambda=\lambda^{\prime}-\lambda=\frac{h}{m_ec}(1-\cos\theta)\]

\[
\nu_0 = \frac{\phi_0}{h}
\]

1. For a given photosensitive material, there is no photoelectric emission below the threshold frequency (v₀​). The threshold frequency is different for different metals.
2. For a given photosensitive material and frequency of incident radiation (above threshold frequency), the photoelectric current is directly proportional to the intensity of incident light.
3. Above the threshold frequency v₀​, the maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident radiation, but is independent of intensity of incident radiation.
4. The emission of a photoelectron is an instantaneous process. There is no time lag between the irradiation of the metal surface and emission of photoelectrons.

1. According to de-Broglie, every particle of matter has both particle as well as wave properties associated with it.
2. De-Broglie proposed that a moving material particle of total energy EE and momentum pp has a wave associated with it.
3. Wave-particle duality implies that all moving particles have an associated frequency, an associated energy, and an associated momentum.

1.  The experiment verified the de-Broglie hypothesis.
2. In this experiment, the wave nature of electron particles was studied with the help of a nickel crystal.
3. Electrons undergo interference and diffraction phenomena and produce alternate bright and dark rings.
4. When accelerating potential V = 54 V:
   λ = 0.165 nm (Experimental value)
   λ = 0.167 nm (Theoretical value from de-Broglie hypothesis)

• Wave theory could not explain the instant emission of electrons; it predicted a time delay.
• It said higher intensity should give higher kinetic energy, but actually, kinetic energy depends on frequency, not intensity.
• Wave theory predicts emission at any frequency when intensity is high, but emission occurs only when the frequency is above the threshold frequency (ν₀).
• Even very low intensity light causes immediate emission, which contradicts wave theory.
• Hence, the photoelectric effect supported the particle (quantum) nature of light rather than the wave theory.

• Electrons are emitted only if the light frequency is greater than a minimum value, the threshold frequency (ν₀), which differs for different metals.
• Emission of electrons is instantaneous; there is no time delay between light falling and electrons coming out.
• At a fixed frequency, photocurrent increases with increasing light intensity.
• Photocurrent increases with accelerating potential and then becomes constant; this maximum value is called the saturation current.
• Saturation current depends on light intensity, not on its frequency (if ν > ν₀).
• The maximum kinetic energy of emitted electrons depends only on the frequency of light, not on its intensity.
• Stopping potential is the minimum negative potential needed to stop the photocurrent; it depends on frequency, not on intensity.

• Einstein extended Planck’s idea and proposed that light behaves as particles called photons, each carrying energy hνh\nuhν.
• A photon gives all its energy to a single electron; emission occurs only if this energy is equal to or greater than the work function of the metal.
• Photoelectric emission is instantaneous because energy transfer from photon to electron occurs in a single interaction.
• The intensity of light controls the number of emitted electrons (photocurrent), while the frequency controls the maximum kinetic energy of the electrons.
• Einstein’s photon theory successfully explained threshold frequency, stopping potential, saturation current, and all experimental observations of the photoelectric effect.