Revision: 12th Std >> Dual Nature of Radiation and Matter MAH-MHT CET (PCM/PCB) Dual Nature of Radiation and Matter

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 known as the photoelectric effect. 

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 minimum value of energy required for the emission of photoelectrons from a metal surface is called the Work Function.

The retarding potential (–V₀) for which the photocurrent becomes zero is called the Stopping Potential.

The limit of photocurrent at which the increase in photocurrent stops even if the collector plate potential (V) is increased is called the Saturation Current.

The stopping potential is defined as the potential necessary to stop any electron from reaching the other side.

Threshold frequency is the lowest frequency of electromagnetic radiation that will result in the emission of electrons from a specified metal surface.

The minimum value of frequency of incident radiation required for the emission of photoelectrons from a metal surface is called the Threshold Frequency.

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 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.

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

The tiny unit (packet or quantum) of radiant energy having energy equal to hvhv, where hh is Planck's constant and vv is the frequency of radiation, is called a Photon.

\[\phi_0=hv_0=h\frac{c}{\lambda_0}\]

\[V_0=\frac{hv}{e}-\frac{\phi_0}{e}=\frac{K.E_{max}}{e}\]

hv = \[\frac {1}{2}\]​m\[\ v_{max}^2\] + ϕ_0​; K . E_max = hv − 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 = hv

• When light of frequency ≥ threshold frequency (ν₀) falls on a metal surface, electrons are emitted.
• If ν < ν₀ → no emission, regardless of intensity.
• The threshold frequency (ν₀) varies with metal.
• Energy equation: \[h\nu=h\nu_0+\frac{1}{2}mv^2\]
• Maximum kinetic energy depends only on frequency, not on intensity.
• Number of emitted electrons depends on intensity (for ν ≥ ν₀).
• Emission of electrons is instantaneous (no time lag).
• Increasing frequency increases the kinetic energy of electrons.
• Increasing intensity increases the number of electrons, not their energy.
• The photoelectric effect proves the particle (quantum) nature of light.

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)

• Proposition:
  Energy is emitted in packets (quanta).
  At higher frequencies, the energy of a packet is large.
• Planck assumed that atoms behave like tiny oscillators that emit electromagnetic radiation only in discrete packets of energy E = hv, where v is the frequency of the oscillator.
• The emissions occur only when the oscillator makes a jump from one quantized level of energy to another of lower energy.
• This model of Planck formed the basis for explaining the observations of the photoelectric effect.