Answer to Question #151561 in Electricity and Magnetism for Iftikhar Ahmed

Question

(i) Describe the Einstein theory of photo electric effect and draw the circuit diagram of the 

apparatus to find Plank’s constant by Photo electric effect.

Answer 1

Einstein introduced an idea that energy distribution in radiation is discrete so radiation propagates in form of discrete packets (Photon) of energy. Energy of each packet is $h\times\nu$.

To support his idea of discrete nature of radiation, Einstein argued that photoelectric effect can be explained using concept of radiation.

in 1887 Hertz had observed that when UV light falls on alkali metals then electrons are immediately emitted. This phenomena is called Photo Electric Effect(PEE). Later on studied made on PEE in details and following results were found.

1. If Degeneracy (frequency) of radiation is not changed and Intensity of radiation is varying then Kinetic energy (K.E) of electron does not changes.

If $\nu$ is varied then K.E of Photo Electric varies.

Einstein's Explanation of PEE

Einstein said that PEE occurs when one quantum (Photon) of radiation is absorbed by an electron. This process takes place near metal surface.

Equation of PEE

$$K.E=h\times\nu- W$$

where

• "W" is the work function of metal. It is the minimum energy lost by electron while coming out of surface.
• $h\nu$ is the energy of incident radiation of frequency $\nu$ .

If V_s is the stopping voltage (applied reversed voltage to make current zero) then

$$(K.E)_{max}=e\times V_s$$

Calculation of Planck's Constant

From above two equation, we can write

$$e\times V_s=h\times\nu-W\\ V_s=\cfrac{h\times\nu}{e}-\cfrac{W}{e}$$

Now we perform PEE for different frequency and making current zero by applying Stopping Potential (V_s) and make observation for different pair of ($V_s, \nu$ ). We plot the graph between $V_s$ and $\nu$ .

Graph is linear and its slope is $M=\cfrac{h}{e}.$

Multiplying slope by electronic charge gives us numerical value of Planck's Constant.

$h=M\times e$ .