Quantum Physics: Work Function

In summary, the American physicist Robert A. Millikan won the 1923 Nobel Prize for his work on the photoelectric effect. Using observations of the maximum kinetic energy of electrons ejected with different wavelengths of light, it is possible to calculate the work function of a hypothetical metal without knowing the value of Planck's constant. To solve for the work function, one must first determine the stopping potential, which is the potential required to stop electrons with the maximum kinetic energy.
  • #1
TJDF
27
0

Homework Statement



The American physicist Robert A. Millikan (1868-1953) won the 1923 Nobel Prize in physics, in part for his work on the photoelectric effect. Assume that Millikan observed for a hypothetical metal a maximum kinetic energy of 0.535 eV when electrons were ejected with 431.7 nm light. When light of 258.6 nm was used, he observed a maximum kinetic energy of 2.52 eV. Using these results, calculate the work function, W0, for the metal, without knowing the value for Planck's constant.

Homework Equations



Vo = [(h/e)*f]-(θ/e)

where θ is the work function.

The Attempt at a Solution



Frequency 1 (using wavelength 1) = 6.94927e14 Hz
Frequency 2 (using wavelength 2) = 1.1601e15 Hz

Delta Frequency = 4.65173e14

Energy 1 (using eV1) =8.571644e-20 J
Energy 2 (using eV2) =4.0375e-19 J

Delta Energy = 3.18032e-19

thus, Delta Energy over Delta Frequency gives me my experimental h...
h = 6.83685e-34 Js

That's all fine and good... but

I have NO idea how to solve for the work function.

Greatly appreciate a reply, this is my last question of the day.
 
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  • #2
Hmmm... still no luck on this one yet. ideas?
 
  • #3
some progress...

so e = 1.60e-19 C

f will equal 0... so...

Vo = θ/e ; θ = e*Vo = (1.60e-19J)*( ? V)

hmmmm... how to figure out Vo?
 
  • #4
Hi TJDF,

TJDF said:
some progress...

so e = 1.60e-19 C

f will equal 0... so...

Vo = θ/e ; θ = e*Vo = (1.60e-19J)*( ? V)

hmmmm... how to figure out Vo?


Vo is the stopping potential, which is the potential required to stop even those electrons with the maximum kinetic energy. In that case, the maximum kinetic energy is being converted completely into potential energy. Do you see how to calculate Vo?

(You might also find some other forms of the photoelectric effect equation that have the maximum kinetic energy explicitly, instead of the stopping potential; those forms would be more straightforward for this problem.)
 

What is quantum physics?

Quantum physics is a branch of physics that studies the behavior and interactions of particles at a subatomic level. It is based on the principles of quantum mechanics, which describes the behavior of matter and energy on a very small scale.

What is the work function in quantum physics?

The work function in quantum physics is the amount of energy needed to remove an electron from a solid material. It is a fundamental concept in understanding the photoelectric effect, which is the emission of electrons from a material when exposed to light.

How is the work function related to the energy of an electron?

The work function is directly related to the energy of an electron. The energy of an electron is equal to the work function plus its kinetic energy. This means that if the energy of an electron is greater than the work function, the electron can escape from the material.

What factors affect the work function?

The work function is affected by the type of material, its surface structure, and the intensity of the incident light. Different materials have different work functions, and a rougher surface can have a lower work function due to the presence of more surface defects. Additionally, increasing the intensity of the incident light can also decrease the work function.

How is the work function measured?

The work function is typically measured using a device called a photocell or photometer. This device measures the current produced when light of a certain frequency is shone onto a material. By varying the frequency of the light, the work function can be determined by finding the point at which the current drops to zero.

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