In a photoelectric experiment in which monochromatic light and a sodium photocathode are used, w

step 1 Hello and welcome to this video solution of numerate. So here we are given that in a photoelectr

In a photoelectric experiment in which monochromatic light...

Key Concepts

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a material (typically a metal) when it is exposed to light of sufficiently high frequency. This process demonstrates the particle-like nature of light, as only photons with energy greater than a specific threshold (the work function of the material) can eject electrons. It plays a key role in establishing the concept of quantized energy packets in quantum mechanics.

Stopping Potential

Stopping potential is the minimum voltage required to halt the most energetic photoelectrons emitted from a surface during the photoelectric effect. By measuring this voltage, one can determine the maximum kinetic energy of the ejected electrons, since the product of the stopping potential and the electron charge equals that kinetic energy. This measurement is crucial for experiments that determine quantities like Planck's constant and the material's work function.

Work Function

The work function is the minimum energy needed to remove an electron from the surface of a material. In the context of the photoelectric effect, it represents the energy barrier that must be overcome by the photon’s energy in order to liberate an electron from the metal. Its value is intrinsic to the material and is typically expressed in electron volts (eV).

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency (E = hf). It is a key parameter in the photoelectric effect, where the measurement of stopping potentials and corresponding frequencies or wavelengths of incident light allows for an experimental determination of its value.

Threshold Wavelength

The threshold wavelength is the maximum wavelength (or minimum frequency) of light that can cause photoemission from a material. It is directly related to the work function, as light with a wavelength longer than the threshold does not carry enough energy per photon to overcome the work function. This concept is essential for understanding why only photons with sufficient energy can liberate electrons.

Transcript

00:01 Hello and welcome to this video solution of numerate.

00:03 So here we are given that in a photoelectric experiments in which monochromatic light and a sodium photocathode are used.

00:14 We find a stopping potential of let's say v1 that is equal to 1 .85 volts for a wavelength lambda 1 we can write that is 3000 armstrong right and in the other one you have got v2 that is 0 .82 volts and lambda 2 that's around 4000 armstrong right.

00:41 From this data you have to determine the value of the planck constant the work function of the sodium in an electron volt right and the threshold wavelength.

00:52 So a to determine the planck's constant you have to apply the formula the kinetic energy k max will be equal to the energy supplied by the photon minus the work function phi right.

01:09 K max will be equal to ev1 this is the stopping potential that is given by hc by lambda 1 minus phi will remain constant in both the cases right.

01:23 Now this is ev2 that is equal to hc by lambda 2 minus phi right.

01:29 So you have got both this equation.

01:32 Now if you 1 and 2 from 1 and 2 if you just remove this phi okay eliminate this phi then h will come out to be as per the expression it's e times of you will be having e1 minus v2 over c times 1 by lambda 1 minus 1 by lambda 2 right.

02:00 So this is what you have.

02:02 Now what you can do is you can simply plug in all these values now like you have got 1.

02:13 You don't need to have this you can keep this e times of this is 1 .85 minus v2 is you have got 0 .82 right over c by c we can write like in terms of nanometers per second which is 3 times of 10 to the power of minus sorry 17 nanometers per second.

02:44 What i am doing is i just keeping electron volt and second right or sorry here we are given armstrong so armstrong per 7 you can so it's 10 to the power of 18 now per second here you will be having the values in armstrong which is 3000 minus 1 by 4000 right armstrong 1 by armstrong sort of like this right.

03:27 So if you just this will be the upper one will be in electron volts right...

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