Modern Physics: Mastering Physics: The Photoelectric Effect Experiment

Learning Goal: To understand the experiment that led to the discovery of the photoelectric effect.
In 1887, Heinrich Hertz investigated the phenomenon of light striking a metal surface, causing the ejection of electrons from the metal. The classical theory of electromagnetism predicted that the energy of the electrons ejected should have been proportional to the intensity of the light. However, Hertz observed that the energy of the electrons was independent of the intensity of the light. Furthermore, for low enough frequencies, no electrons were ejected, no matter how great the intensity of the light became. The following problem outlines the methods used to investigate this new finding in physics: the photoelectric effect.

Suppose there is a potential difference between the metal that ejects the electrons and the detection device, such that the detector is at a lower potential than the metal. The electrons slow down as they go from higher to lower electric potential; since they must overcome this potential difference to reach the detector, this potential is known as the stopping potential. To reach the detector, the initial kinetic energy of an ejected electron must be greater than or equal to the amount of energy it will lose by moving through the potential difference.

Part A

If there is a potential difference

between the metal and the detector, what is the minimum energy E_min

that an electron must have so that it will reach the detector?

Express your answer in terms of

and the magnitude of the charge on the electron,

ANSWER:

$eV$

For the incident light to cause the ejection of an electron, the light must impart a certain amount of energy to the electron to overcome the forces that constrain it within the metal. The minimum amount of energy required to overcome these forces is called the work function phi

. Different metals will have different values for phi

. For an electron to reach the detector, the light must impart enough energy for the electron to overcome both the work function and the stopping potential.

Part B
Suppose that the light carries energy . What is the maximum stopping potential that can be applied while still allowing electrons to reach the detector?

Express your answer in terms

, and

ANSWER:

$\frac{\left(E_{light}-{\phi}\right)}{e}$

Part C

Classical electromagnetism predicted that V_0

should have increased as the intensity of the incident light increased. On the contrary, it was found that V_0

increased as the frequency

of the light increased. The voltage V_0

was found to obey the following linear relationship:

$V_{0} = mf - b$ ,

where

and

are numerical constants (representing the slope and the intercept, respectively). By comparing this equation to your answer from Part B, find an expression for the intercept

. (Notice that $mf$ in this equation changes with different light but

is a constant of the metal.)

Express your answer in terms of phi

and

ANSWER:

$\frac{{\phi}}{e}$

Part D

In a 1905 paper that later won him a Nobel Prize, Albert Einstein postulated that the energy of light was proportional to its frequency. The constant of proportionality turned out to be Planck's constant