Quick Revision Notes

Class 12 Physics: Dual Nature of Radiation and Matter

MP Board (NCERT Curriculum)

Electron Emission: The phenomenon of emission of electrons from a metal surface is called electron emission.
Types of Emission:
1. Thermionic Emission: By supplying thermal energy.
2. Field Emission: By applying a very strong electric field.
3. Photoelectric Emission: By shining light of suitable frequency.
4. Secondary Emission: By bombardment of fast-moving electrons.
Work Function ($\phi_0$): The minimum amount of energy required by an electron to just escape from the metal surface is called the work function of that metal. It is measured in electron volts (eV).
- Formula: $\phi_0 = h \nu_0$
- Where $h$ is Planck's constant and $\nu_0$ is the threshold frequency.

Energy of a Photon: E = h\nu = \frac{hc}{\lambda}
- $h = 6.63 \times 10^{-34} \text{ J s}$ (Planck's Constant)
- $c = 3 \times 10^8 \text{ m/s}$ (Speed of light)
- $\nu =$ Frequency, $\lambda =$ Wavelength
Momentum of a Photon: p = \frac{E}{c} = \frac{h}{\lambda}

The phenomenon of emission of electrons from metal surfaces when light of suitable frequency falls on them is called the photoelectric effect.

Important Terms:

Threshold Frequency ($\nu_0$): The minimum frequency of incident light below which no photoelectric emission takes place, no matter how intense the light is.
Threshold Wavelength ($\lambda_0$): The maximum wavelength of incident light above which photoelectric emission stops.
Stopping Potential ($V_0$): The minimum negative (retarding) potential applied to the anode at which the photoelectric current becomes zero.

According to Einstein, maximum kinetic energy of emitted photoelectrons is: K_{max} = E - \phi_0

K_{max} = h\nu - h\nu_0 = h(\nu - \nu_0)

In terms of Stopping Potential ($V_0$): K_{max} = e V_0

Therefore, Einstein's equation can also be written as: e V_0 = h\nu - \phi_0 e V_0 = \frac{hc}{\lambda} - \phi_0

De Broglie Hypothesis: Waves are associated with moving material particles (like electrons, protons, etc.). These waves are called matter waves or de Broglie waves.
De Broglie Wavelength ($\lambda$): \lambda = \frac{h}{p} = \frac{h}{mv}
- Where $m =$ mass of the particle, $v =$ velocity, $p =$ momentum.

Alternative Forms of De Broglie Wavelength:

In terms of Kinetic Energy ($K$): \lambda = \frac{h}{\sqrt{2mK}}
In terms of Accelerating Potential ($V$): \lambda = \frac{h}{\sqrt{2meV}}
- For an electron, substituting values of $h$, $m$, and $e$: \lambda = \frac{12.27}{\sqrt{V}} \text{ \AA} (where $V$ is in volts)

Variation of Photoelectric Current vs Intensity of Light: Linear straight line (Current is directly proportional to intensity).
Variation of Photoelectric Current vs Anode Potential: Current increases and then reaches a saturation limit.
Variation of Stopping Potential vs Frequency of Incident Light: A straight line cutting the frequency axis at threshold frequency ($\nu_0$).

$1 \text{ eV} = 1.6 \times 10^{-19} \text{ Joules}$
$h = 6.63 \times 10^{-34} \text{ J}\cdot\text{s}$ or $4.14 \times 10^{-15} \text{ eV}\cdot\text{s}$
Mass of electron ($m$) $= 9.1 \times 10^{-31} \text{ kg}$