Photoelectric Effect: The Quantization of Energy and Light

OBJECTIVE: To observe, analyze and understand the quantum phenomenon known as the Photoelectric Effect. To calculate the values of Planck's constand and the work function.

EQUIPMENT: Photoelectric Effect box, DC power supply, multimeters (2), cables

INTRODUCTION:

Here are two reasons to study the Photoelectric Effect: one, it is the basis on which many of today's optoelectronic devices work and two, it can give you insight into how this experiment, together with Blackbody Radiation, Compton, and Atomic Spectra experiments, led to the mathematical description of how matter and energy behave on a very small scale, Quantum Mechanics.

Digital cameras, automatic garage door openers, notebook computer displays and light-emitting diodes (LEDs) all operate on the Photoelectric Effect - the ejection of negative particles from a metal upon which light is incident. Ironically, Heinrich Hertz discovered the phenomenon in 1887 during an experiment in which he produced and detected electromagnetic waves, simultaneously confirming Maxwell's theory while leading to the particle description of light. Philip Lenard identified the particles experimentally as electrons in 1900, but it took the genius of Einstein to explain the phenomenon in a 1905 paper for which he was awarded the Nobel Prize, and which helped usher in the era known as "Modern Physics'.

The Apparatus

Increasing the light intensity also increases the maximum current. In fact, they are proportional. This jibes well with classical physics since doubling the energy on E doubles the number of ejected electrons. Now, if C is kept at a lower potential than E, electrons are repelled from C. Remember from the E&M Forces lab that an electron gains kinetic energy eV when accelerated through a potential difference V - only electrons with kinetic energies greater than e|V| (energy can't be negative) can reach C.

Look at the graph above, in which photoelectric current vs. potential difference is plotted for three different intensities of light (by varying the lamp-metal distance). Notice that for all light intensities there is no photoelectric current when the voltage is greater than V₀=0.8. V₀ is called the stopping potential. Since the initial electron's kinetic energy is lost in overcoming the stopping potential, we can relate the maximum kinetic energy of the electron:

Now, what does all this have to do with Quantum Mechanics? Look once again at the graph above – V₀ does not depend on the light intensity. If we increase the rate of energy falling on the metal, we don't increase the kinetic energy of the electrons ejected! Einstein theorized that light energy, rather than being spread out like a wave, was quantized into discrete amounts (quanta) of energy , where h is Planck's Constant (4.136 x 10^-15 eV-sec or 6.626 x 10^-34 J-sec) and f is the frequency of the light. When one of these quanta, also known as a photon, enters the metal, all of its energy is given to an electron. This would explain why intensifying the light results in higher numbers of electrons rather than higher electron energies.

There are other energy losses to bear in mind other than the energy required to traverse the cathode-collector potential – the electron loses energy going through the metal before hitting its particular electron, and the electron has to overcome the binding energy of the metal, denoted by. (You can think ofas being similar to gravitational or electrical potential – the energy required to move a charge or mass from where it is to someplace very far away.) Keeping these in mind, the maximum energy of the electron (others will lose more energy it traveling through the metal) is and Einstein's equation for the photoelectric effect is:

(photon energy) -> (K.E needed to just break stopping pot.)+ (energy needed to leave metal)

We can rewrite Einstein's equation in form as;

If we plot V₀ as a function of , a graph will yield a straight line whose slope does not depend on; it is independent of the material ejecting the electron. Note also that we can determine the work function, since the Y-intercept is. See graph below:

Stopping Potential, V

Frequency, Hz

Labeled in the above graph is , the threshold frequency. Photons which have frequencies lower than this do not have enough energy to eject an electron from the metal. The relationship between and can be obtained by setting V₀=0 in

the photoelectric equation:

The value is usually expressed in eV-Å or eV-nm, since wavelengths are typically expressed in Anstroms or nanometers:

hc=1240 eV-nm = 12,400 eV- Å

Visible light ranges from 400-800 nm (4000-8000 Å), so most work functions are on the order of a few electron volts:

PROCEDURE

Look at the photo labeled “The Apparatus”. The box houses the photoelectric tube and circuit picture in the schematic on page 2. The cables are pre-wired; please don't change any connections. However, here are the connections in case they have been tampered with - on the metal box (housing the photoelectric tube), the labeled jacks are connected to:

Vcurr --> red jack on Voltmeter

Vr--> red jack on other Voltmeters

Gnd--> ground on Power Supply, ground on Voltmeter

-12--> -12 on Power Supply

+12--> +12 on Power Supply

(the remaining Voltmeter ground should be connected to the remaining Power Supply ground)

Two multimeters, connected to the two green jacks, monitor the photoelectric voltage V_curr and potential difference V_R. The photoelectric current is too small for your multimeter to measure directly – instead, an operational amplifier in the box outputs V_curr, which is proportional to the current. You can obtain the current from the equation I=V_curr/6.6 x 10⁷Ω or I=V_curr/2.0 x 10⁸Ω (see top of box for conversion factor).

The blue knob varies V_R. This will range from roughly 0 to 3.2 V. At the top of a box is a dial on which seven filters are mounted (yes, that is a Gerber baby food lid – physicists do recycle). Each filter will transmit light of a specific wavelength that will strike the photoelectric tube; the wavelengths are marked on the dial. Do not assume that a filter lined up with the dial mark on the box perfectly aligns it wth the hole in the box – "fine tune" the dial until you get maximum V_curr with each reading. Position the desk lamp a few inches above the dial (don't turn it on yet) and turn the power supply and voltmeters on.

Qualitative Observations & Predictions

Turn the blue knob fully counterclockwise (zero stopping potential). Turn the dial to the 500 nm filter. You will be asked to make a series of predictions, which are written in the hand-in sheet at the end of this write-up. Your instructor will not penalize you for incorrect predictions, and will just check to see that you attempted a prediction.

Quantitative Observations

(WARNING – THE DESK LAMP CAN GET QUITE HOT TO THE TOUCH)

I vs. V

You will vary V_R (using blue knob) and see how V_curr changes, for two different light intensities. Select the 500 nm filter on the dial. Keep the light a few inches above the box. Vary V_R in 0.1 Volt intervals, from 0 to about 1.4 V, each time recording the V_curr. Make sure you do not change the orientation of lamp or box during this time, as you may may render your results useless.

Repeat the above, after raising the lamp to approximately twice the original distance above the box (several inches). You should then generate two plots on one graph, one for each light intensity.

V₀ vs. f

You will now vary (using filter dial) and see how V₀ changes. Starting at the highest wavelength (which corresponds to the lowest frequency), vary V to obtain zero V_curr. Once you have obtained zero V_curr, note your V_r at that point – that will be your stopping potential V₀. Repeat for the other filters and generate your plot. Again, make sure you move neither box nor lamp during the measurements.