Q.A mercury lamp is a convenient source for studying frequency dependence of photoelectric emission, since it gives a number of spectral lines ranging from the UV to the red end of the visible spectrum. In our experiment with rubidium photo-cell, the following lines from a mercury source were used: $\lambda_1 = 3650\ \text{Å}, \lambda_2 = 4047\ \text{Å}, \lambda_3 = 4358\ \text{Å}, \lambda_4 = 5461\ \text{Å}, \lambda_5 = 6907\ \text{Å}$, The stopping voltages, respectively, were measured to be: $V_{01} = 1.28\ \text{V}, V_{02} = 0.95\ \text{V}, V_{03} = 0.74\ \text{V}, V_{04} = 0.16\ \text{V}, V_{05} = 0\ \text{V}$. Determine the value of Planck's constant $h$, the threshold frequency and work function for the material.

Photon Energy: The Energy Carried by Light

Light does not carry its energy in a continuous stream. It comes in discrete packets — like individual drops instead of a steady hose. Each packet is called a photon: the smallest possible unit of light of a given frequency. You cannot have half a photon; it is all or nothing.

The Intuition: Colour Determines Energy

Red light and blue light are both light, but they behave differently — blue light causes sunburn and drives chemical reactions more readily than red. The reason is that the colour (frequency) of light directly fixes how much energy each photon carries, and blue photons carry more energy than red photons.

The Planck–Einstein Relation

The energy $E$ of a single photon is directly proportional to its frequency $f$, and inversely proportional to its wavelength $\lambda$:

Where:

• $E$ = energy of one photon (joules, J)
• $f$ = frequency (hertz, Hz)
• $\lambda$ = wavelength (metres, m)
• $c$ = speed of light in vacuum ($3.00 \times 10^8$ m/s)
• $h$ = Planck's constant ($6.626 \times 10^{-34}$ J·s)

What This Tells You

1. Higher frequency = higher energy. Gamma rays have extremely energetic photons; radio waves have very low-energy photons.
2. Shorter wavelength = higher energy. Ultraviolet photons are more energetic than visible-light photons; infrared photons are less.
3. Energy is quantised. Light energy comes in fixed packets — you can have 1, 2, or 1000 photons, but never 0.5. This was Max Planck's revolutionary idea of 1900.

This is why UV light causes sunburn (UV photons carry enough energy to damage DNA, while visible photons do not), why X-ray photons are energetic enough to pass through soft tissue but get absorbed by bone, and why a photon needs enough energy to actually break a bond or drive a photochemical/biological reaction, rather than merely wavelength-dependent intensity.

A Concrete Example

Since $E = \dfrac{hc}{\lambda}$, energy is inversely proportional to wavelength, so the shorter-wavelength blue photon carries more energy:

• Red: $E_{\text{red}} = \dfrac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{700 \times 10^{-9}} \approx 2.84 \times 10^{-19}$ J …