Photons — Revision Notes

⚡ 30-Second Revision

Photon Energy: — $E = h

u = hc/lambda$

Photon Momentum: — $p = h/lambda = E/c$
Planck's Constant: — $h = 6.626 \times 10^{-34},\text{J}cdot\text{s}$ (or $1240,\text{eV}cdot\text{nm}$ for $hc$)
Speed of Light: — $c = 3 \times 10^8,\text{m/s}$
Photoelectric Equation: — $h

u = phi_0 + K_{max}$

Work Function: — $phi_0 = h

u_0 = hc/lambda_0$(where$ u_0$is threshold frequency,$lambda_0$ is threshold wavelength)

Maximum Kinetic Energy: — $K_{max} = eV_s$ (where $V_s$ is stopping potential)
Photon Properties: — Zero rest mass, travels at $c$, electrically neutral, possesses spin $1hbar$.
Intensity: — Proportional to number of photons per unit area per unit time.

2-Minute Revision

Photons are the fundamental, massless packets of electromagnetic energy. Their energy is quantized, given by $E = h u$ or $E = hc/lambda$, where $h$ is Planck's constant, $u$ is frequency, $lambda$ is wavelength, and $c$ is the speed of light.

Despite zero rest mass, photons carry momentum, $p = h/lambda = E/c$. They are electrically neutral and always travel at the speed of light in a vacuum. The concept of photons is crucial for explaining the photoelectric effect, where light interacts with matter as discrete particles.

Einstein's photoelectric equation, $h u = phi_0 + K_{max}$, describes this interaction, relating photon energy to the work function ($phi_0$) of the metal and the maximum kinetic energy ($K_{max}$) of the emitted electrons.

The work function is the minimum energy required to eject an electron, corresponding to a threshold frequency ($u_0$) or maximum threshold wavelength ($lambda_0$). Light intensity is proportional to the number of photons, affecting the number of emitted electrons, while photon frequency determines the energy of individual photons and thus the kinetic energy of the photoelectrons.

Remember unit conversions, especially between Joules and electron volts.

5-Minute Revision

Photons are the elementary particles of light, representing the quantum nature of electromagnetic radiation. Each photon is a discrete packet of energy, $E = h u = hc/lambda$, where $h$ is Planck's constant ($6.

626 imes 10^{-34}, ext{J}cdot ext{s}$),$ u$is frequency,$lambda$is wavelength, and$c$is the speed of light ($3 imes 10^8, ext{m/s}$). A useful constant for calculations is$hc approx 1240, ext{eV}cdot ext{nm}$.

Photons have zero rest mass, always travel at $c$ in a vacuum, are electrically neutral, and carry momentum $p = h/lambda = E/c$. This momentum is responsible for radiation pressure.

The most significant application for NEET is the photoelectric effect, where light shining on a metal surface ejects electrons. Key observations that classical wave theory failed to explain, but the photon theory successfully did, include:

1
**Threshold frequency ($

u_0$):** Below this frequency, no electrons are emitted, regardless of intensity. This is because individual photons lack sufficient energy to overcome the metal's work function ($phi_0 = h u_0$).

1
Instantaneous emission: — Electron ejection is immediate, as energy transfer from a photon is 'all-or-nothing' to a single electron.
2
Kinetic energy dependence: — The maximum kinetic energy ($K_{max}$) of photoelectrons depends only on the frequency of light, not its intensity. Higher frequency means more energetic photons, leading to higher $K_{max}$.
3
Intensity dependence: — The number of photoelectrons emitted is proportional to the intensity of light, as higher intensity means more photons striking the surface per unit time.

Einstein's photoelectric equation summarizes this: $h u = phi_0 + K_{max}$. Here, $h u$ is the incident photon energy, $phi_0$ is the work function (minimum energy to eject an electron), and $K_{max}$ is the maximum kinetic energy of the emitted electron. The maximum kinetic energy can also be expressed as $K_{max} = eV_s$, where $e$ is the elementary charge and $V_s$ is the stopping potential (the minimum negative potential required to stop all photoelectrons).

Example: If a photon of $4,\text{eV}$ strikes a metal with a work function of $2.5,\text{eV}$, the maximum kinetic energy of the emitted electron would be $K_{max} = 4,\text{eV} - 2.5,\text{eV} = 1.5,\text{eV}$. The stopping potential would then be $V_s = 1.5,\text{V}$.

Remember to be meticulous with unit conversions, especially between Joules and electron volts ($1,\text{eV} = 1.6 \times 10^{-19},\text{J}$). Conceptual questions often test the wave-particle duality, asking which phenomena support which nature of light.

Prelims Revision Notes

Photons: Key Concepts for NEET UG

1. Definition and Nature:

Photon: — The quantum (discrete packet) of electromagnetic energy.
Rest Mass: — Zero ($m_0 = 0$). Photons are never at rest.
Speed: — Always travels at the speed of light ($c = 3 \times 10^8,\text{m/s}$) in a vacuum.
Charge: — Electrically neutral (zero charge). Not deflected by electric or magnetic fields.
Spin: — Possesses intrinsic angular momentum (spin $1hbar$). They are bosons.
Wave-Particle Duality: — Exhibits both wave-like (diffraction, interference) and particle-like (photoelectric effect, Compton effect) properties.

2. Photon Energy and Momentum:

Energy ($E$): — Directly proportional to frequency ($

u$), inversely proportional to wavelength ($lambda$). *$E = h u$*$E = hc/lambda$* Where$h$is Planck's constant ($6.626 imes 10^{-34}, ext{J}cdot ext{s}$).

Momentum ($p$): — Possessed despite zero rest mass.

* $p = E/c$ * $p = h/lambda$

Useful Constant: — $hc approx 1240,\text{eV}cdot\text{nm}$ (for quick calculations when $lambda$ is in nm and $E$ in eV).

3. Photoelectric Effect:

Definition: — Emission of electrons from a metal surface when light of sufficient frequency falls on it.
Key Observations (explained by photon theory):

* **Threshold Frequency ($u_0$):** Minimum frequency of incident light below which no photoelectrons are emitted, regardless of intensity. Corresponds to threshold wavelength ($lambda_0 = c/ u_0$).

* **Work Function ($phi_0$):** Minimum energy required to eject an electron from the metal surface. $phi_0 = h u_0 = hc/lambda_0$. * Instantaneous Emission: Photoelectron emission is instantaneous if $u ge u_0$.

* **Kinetic Energy ($K_{max}$):** Maximum kinetic energy of emitted photoelectrons depends only on the frequency of incident light, not its intensity. * Photocurrent: Proportional to the intensity of incident light (more photons $ightarrow$ more electrons).

Einstein's Photoelectric Equation: — $h

u = phi_0 + K_{max}$*$K_{max} = h u - phi_0$*$K_{max} = rac{hc}{lambda} - rac{hc}{lambda_0}$

Stopping Potential ($V_s$): — The minimum negative potential applied to the anode that stops the most energetic photoelectrons. $K_{max} = eV_s$.

4. Intensity of Light:

Intensity ($I$) is the power per unit area ($P/A$).
$I = \frac{\text{Number of photons per second} \times E_{photon}}{\text{Area}}$.
Higher intensity means more photons per unit time, leading to more photoelectrons (if $

u ge u_0$), but does not change the energy of individual photons or$K_{max}$.

5. Unit Conversions:

$1,\text{eV} = 1.602 \times 10^{-19},\text{J}$
$1,\text{nm} = 10^{-9},\text{m}$

Practice Tip: Focus on numerical problems involving the photoelectric equation and unit conversions. Understand the graphs related to the photoelectric effect (e.g., $K_{max}$ vs. $u$, photocurrent vs. $V_s$).

Vyyuha Quick Recall

Photons Have Energy, Momentum, No Rest Mass, Speed C, No Charge.

Photons
Have Energy ($E=h

u$)

Momentum ($p=h/lambda$)
No Rest Mass
Speed C ($c$ in vacuum)
No Charge