Calculate the value of (a) Planck's constant and (b) the...

Name: Problem 13, Chapter 27: College Physics
Uploaded: 2020-05-20T18:54:52-08:00
Duration: 5 min 23 s
Channel: Guilherme Barros
Description: Calculate the value of (a) Planck's constant and (b) the work function of the metal from the data obtained by Robert A. Millikan in 1916 . Millikan was attempting to disprove the Einstein photoelectric equation; instead he found that his data supported Einstein's prediction.

Calculate the value of (a) Planck's constant and (b) the work function of the metal from the data obtained by Robert A. Millikan in 1916 . Millikan was attempting to disprove the Einstein photoelectric equation; instead he found that his data supported Einstein's prediction.

Key Concepts

Photoelectric Effect

The photoelectric effect is a phenomenon where electrons are emitted from the surface of a material, typically a metal, when it is exposed to electromagnetic radiation of sufficient frequency. This concept was crucial in demonstrating the particle nature of light and helped establish the quantum theory by showing that light energy is quantized.

Einstein's Photoelectric Equation

Einstein's photoelectric equation relates the energy of incident photons to the maximum kinetic energy of the emitted electrons, expressed as Kmax = h? - ?, where h is Planck's constant, ? is the frequency of the light, and ? is the work function. This equation was pivotal in confirming that light consists of discrete packets of energy, or quanta.

Planck's Constant

Planck's constant is a fundamental physical constant that establishes the scale at which quantum effects become significant. It appears in the relationship that links the energy of a photon to its frequency, encapsulated in the formula E = h?. Its determination was a key milestone in the development of quantum mechanics.

Work Function

The work function is the minimum amount of energy required to remove an electron from the surface of a material. It is a critical parameter in the photoelectric effect, as it represents the energy barrier that needs to be overcome for electron emission to occur. Understanding the work function is essential for analyzing how different materials interact with light in quantum phenomena.

Transcript

00:01 So for this exercise, we have the original data from millikan from 1916 when he studied the photoelectric effect.

00:12 So in the y -axis, we have the stopping potential v as a function of the frequency f in 10 to the 13 hertz.

00:23 And we also have the frequency.

00:26 Here we have the value of the frequency when the potential is zero.

00:33 That's 43 .9 times 10 to the 13th hertz.

00:41 And we have to calculate from these data both the plunks constant and the work function of the metal silicon was working with.

00:55 So let's do it.

00:57 From the photoelectric effect, we know that e, the charge of the electron times the stopping potential, will be hf minus the work function.

01:12 And since this here is a line, it's a straight line, i'm going to choose any two points.

01:18 The first point i'm going to choose is the pair.

01:21 I'm going to choose v equals 0, and f equals 43 .9 times.

01:30 10 to the 13th 1st.

01:33 And substituting on the photoelectric formula we have 0 equals 43 .9 times 10 to the 13th h minus minus the work function phi.

01:52 So phi can be written as 43 .9 times 10 to the 13th h.

02:03 Okay, and i'm going to choose these two.

02:07 At this point here is the first point i chose, and i found this relation here.

02:12 I'm going to keep it because i'm going to use it very soon.

02:17 And the next point i'm going to choose, just look here in the graph, i'm going to choose this point here that i'm marking in that i'm pointing to in green.

02:29 This point is at approximately v equals 1 .1 volts, and f equals approximately 70 times 10 to the 13th.

02:53 So again, we have, since v is 1 .1 volts, e times v is 1 .1 electron volts...

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