Apparatus:

Experimental setup for the measurement of Planck’s constant, filters of different colors.

Formula Used:

E = hν

Where: h = Planck’s constant ν = Frequency of the light used

Stopping potential equation:

Vs = h/e ν-ϕ

Where: Vs = Stopping potential e = Electronic charge ν = Frequency of the light ϕ = Work function

The slope of the straight line obtained by plotting a graph of Vs as a function of ν yields h/e, and the intercept at ν = 0 gives the work function ϕ of the Cesium-Antimony (Cs-Sb) film.

Theory:

In 1905, it was observed that metals emit electrons when exposed to radiation, a phenomenon known as photoelectric emission. The detailed study of this effect revealed: 1. The emission process depends strongly on the frequency of the radiation. 2. Each metal has a critical frequency below which no electrons are emitted, while frequencies above this threshold always emit electrons. 3. The emission occurs almost instantaneously after the radiation hits the metal, and the number of emitted electrons is proportional to the intensity of the radiation.

These observations provide strong evidence that the electromagnetic field is quantized and consists of energy quanta E = hν, where h is Planck’s constant and ν is the frequency of radiation. These energy quanta are called photons. If electrons are bound inside the metal with an energy eϕ (where ϕ is the work function), it follows that:

• If hν > eϕ, electrons are ejected.
• If hν < eϕ, electron ejection is not possible.

The excess energy of the photon becomes the kinetic energy of the ejected electron, expressed as: hν = (1/2)mv² + eϕ or (1/2)mv² = hν - eϕ

Applying a stopping potential V₀ that completely stops the photoelectrons results in: (1/2)mv² = eVs or eVs = hν - eϕ

Thus:

Vs = h/e ν-ϕ