Photoelectric+Effect

toc = Part 1 =

1. Upon what physical quantity does the color of any glowing body depend? Temperature

2. As the cells in a flashlight get weaker, the filament appears redder. Why? There is more resistance within the flashlight as the cell weakens. Therefore, the temperature decreases in the filament. Therefore, it glows redder.

3. The surface temperatures of Vega, our Sun, and Barnard’s star are 10,000 K, 6,000 K, and 3,000 K respectively. Which of these appears blue in color; red in color; yellow in color? Why? Vega: Blue. Vega is the hottest and therefore emits the shortest wavelength. Sun: Yellow. The sun is in the middle in terms of temperature. Therefore it emits the middling wavelength. Barnard's Star: Red. Barnard's is the coldest and therefore emits the longest wavelength.

4. What is the photoelectric effect? Electrons are emitted from matter as a result of the object's absorption of energy from electromagnetic radiation. Photoelectrons are emitted as a result of photons' energy being absorbed.

5. As a mechanical analog of the photoelectric effect, consider a ball at rest in a depression. If a sufficient amount of energy, E, is given to the ball of mass, m, by the push of the hand, it will roll up the hill and escape with velocity v. Write an equation of energy conservation for this situation and explain each term in the equation by analogy to Einstein’s photoelectric effect equation. W = KE + work function The hand striking the ball represents the light particles contacting the surface of matter in the photoelectric effect. The ball represents the electrons on a given material. If struck with a given amount of energy absorbed from the light, then the ball (electron) will be able to escape the depression (object).

6. An ultraviolet light discharges a negatively charged electroscope. The glass filters the UV light and therefore stops the discharge of photoelectrons.
 * 1) The effect is known as the photoelectric effect.
 * 2) Why isn’t the effect noticed when a glass plate is inserted between the zinc plate and the UV light?

7. What does the work function usually denoted by **// Ψ //** represent? This is the amount of energy that an electron necessitates to escape a given metal.

8. Rewatch the video at about the 7 minute mark. The upper half of the screen shows an electron trying to escape from the surface of the metal. The bottom half is a graph. The vertical axis represents the electric potential energy of the electron. As you watch the video, notice that the electron slides along the bottom line and slips up the edge to the bottom of the work function line. This represents the most energetic electrons, the ones that will escape from the surface if photons strike the surface with energy equal to or greater than the work function. If an electron absorbs a photon of ultraviolet light with energy **//hf//** greater than **// Ψ //**, what will happen to the electron? If an electron absorbs a photon of UV light with energy hf greater than**// Ψ //**, then the electron will escape the metal with energy equivalent to the difference between hf and **// Ψ. //**

9. Use the table of work functions of various metals on page 1. Potassium and Cesium The number of photons in the light would double, but the energy provided by each photon would remain the same. Changing the color would change the amount of energy provided by a single photon. Blue provides more energy than does green.
 * 1) If green light will cause the photoelectric effect to occur in sodium metal, for which other metals listed will it definitely also eject photoelectrons?
 * 1) What would be the effect of doubling the intensity of the light used?
 * 1) What would be the effect of changing the color of the light used, for example, from green to blue or ultraviolet?

10.French Physicist Louis de Broglie questioned, “If light exhibits dual wave-particle behavior, why can’t any particle of matter, such as an electron, exhibit a wave nature?” λ = h/p... Wavelength = h (de Broglie's constant)/momentum Electrons exhibit particles of waves as well as those of particles. Therefore, a half of a wavelength can't exist and orbitals can only exist in whole wavelengths. As particles strike a surface, they produce a spot of light, similar to one that would be produced by wave interference. These correspond to spots of constructive interference
 * 1) How did de Broglie relate a particle’s momentum to its wavelength?
 * 1) In the de Broglie model of the atom, if electrons are viewed as waves circling the nucleus, why do they have to exist in orbits that increase a whole wavelength at a time?
 * 1) Waves produce an interference pattern. How can the pattern be explained in terms of particle of light?
 * 1) To what do the white light spots correspond where the wave pattern hits the screen?

11.The Heisenberg Uncertainty Principle reflects the wave-particle duality of light and matter: The more we know about matter as a particle (well-defined position), the less we know about its momentum (wavelength) and vice versa. We can manipulate the experiment so that we are less certain about the particle's momentum. The momentum of the wave becomes less definite.
 * 1) How can a particle’s location be made more definite?
 * 1) As the position of the wave becomes more definite, what happens to the momentum?

12.What did each of these scientists contribute to Quantum Physics? 13.How does a solar-powered calculator work? Through the photovoltaic effect, voltage is created through the absorption of photons (similar to the photoelectric effect). This allows current to be created and the calculator to be run.
 * 1) Planck- Founder of quantum physics. Discovered black-body radiation. Idea of quanta being discrete packets of light.
 * 2) Einstein- Energy is the same as mass. Explained the photoelectric effect using the idea of quanta.
 * 3) De Broglie- Theorized wave-particle duality of all matter. p = h/λ.
 * 4) Schrodinger- The energy of an electron is always that of a quantized energy level. Electron cloud model.
 * 5) Heisenberg- Heisenberg's uncertainty principle (limits the quantified values of momentum and position of a particle). Also described how quantum leaps occur.

14.How does your cell phone’s digital camera work? The camera basically takes an incoming image and turns it into electrical information in the form of "1's and 0's". In order to do this, each pixel contains three different filters so that the incoming light photons are sorted into each of the three primary colors. The intensity of each color is then recorded at the pixel in question and this determines how much of each of the three colors goes into the single pixel. This happens for every single pixel in order to create a picture.

15.How does a laser work? A laser is a monochromatic, directional source of light. Excited electrons emit light in the form of photons. A laser stimulates this emission of photons and creates a laser (Light Amplification by Stimulated Emission of Radiation).

16.How do solar panels work? Photons' energy absorbed from the light knocks electrons loose within a system of conduction and allows the electrons to flow, thus creating voltage and current.

OK... Got it. Some of these responses are perfunctory, especially the scientists. I hope you know the details better than these explanations demonstrate. ~EB

=Part 2=

1. Suppose you set up the experiment so that the plate is ejecting electrons. Predict which of the following changes to the experiment could increase the maximum initial kinetic energy of the ejected electrons. (Select all that apply) Then test your prediction. > B. Decreasing the intensity of the light beam > C. Increasing the wavelength of light > **D. Decreasing the wavelength of light** > **E. Increasing the frequency of light** > F. Decreasing the frequency of light > **G. Increasing the voltage of the battery** > H. Decreasing the voltage of the battery > I. Replacing the target with a material that has a larger work function > **J. Replacing the target with a material that has a smaller work function**
 * 1) A. Increasing the intensity of the light beam

2. Suppose now you set up the experiment so that the light intensity is non-zero but the plate is NOT ejecting electrons. Predict which of the following changes to the experiment could make the plate start ejecting electrons? (Select all that apply) Then test your prediction. > B. Decreasing the intensity of the light beam > C. Increasing the wavelength of light > **D. Decreasing the wavelength of light** > **E. Increasing the frequency of light** > F. Decreasing the frequency of light > G. Increasing the voltage of the battery > H. Decreasing the voltage of the battery > I. Replacing the target with a material that has a larger work function > **J. Replacing the target with a material that has a smaller work function**
 * 1) A. Increasing the intensity of the light beam

3. What causes the electrons to be ejected from the left plate in this simulation? > **B. The beam of light shining on the plate** > C. Both A and B. > D. Neither A nor B.
 * 1) A. The force exerted on the electrons by the battery

4. Light is shining on a metal and electrons are being emitted. You turn the intensity down very very low. What do you observe? What conclusions can you draw about light, and why? how it is or is not consistent with what you would expect to observe if light matched the classical wave model and with what you would expect to observe if it matched the photon model of light. Less electrons are being emitted, but the electrons are being emitted nonetheless. This means that the amount of a certain wavelength of light being emitted is increased. There are more photons emitted by the light source. This is consistent with the photon model of light for the reasons previously stated. This is not consistent with the wave model of light. The light must have momentum in order for the electrons to be emitted. In the wave model, the light does not have any momentum.

5. Light is shining on a metal plate and electrons are being emitted. Without changing the intensity, you make the wavelength longer and longer. What do you observe? What conclusions can you draw about light, and why? how it is or is not consistent with what you would expect to observe if light matched the classical wave model and with what you would expect to observe if it matched the photon model of light. With the photon model of light, the wavelength is related to energy in that the longer the wavelength, the lesser the energy. With the wavelength model of light, light has no momentum and therefore has no energy. So only the photon model of light allows for the electrons to be emitted.

6. In the photoelectric effect experiment, the graph of current vs battery voltage for a metal with light of a particular frequency shining on it looks like the curve below. This graph represents **current vs voltage** for **200nm light** shining onto **Cadmium (Cd)** which has **a work function of 4.07 eV**.

a) Explain your reasoning for __why__ this curve has the shape that it does. In your answer, you should address: Why is current level at V>0, why does current go to zero at some negative voltage and what determines that voltage, and why does current start decreasing steadily at V<0? Current is defined as charge passed over time passed. And the electrons emitted is not dependent upon the voltage, so the same amount of electrons will be emitted and therefore the same amount will pass through the wire during a given time. At a negative voltage, the electrons emitted will be attracted back to the plate that they were emitted off of. Therefore, less electrons reach the other plate and less charge passes through the wire in a given time.

b) What is the stopping potential in this situation (in eV)? (Remember stopping voltage is expressed as a positive number).

eVs=KEmax = hf - Ψ eVs =(6.626 x 10-34 * 3x108 )/(1.6 x10-19 * 200 x 10-9)- 4.07 = 2.17 eV

c) In the graphs below, the gray curve is always the same and represents the situation you explained in part a (the current vs voltage for 200nm light shining onto Cadmium (Cd) which has a work function of 4.07 eV). The red curves now represent the current vs voltage after a change in the experiment. Use the graphs to answer the questions that follow.

i) If you decrease the wavelength of the light shining onto the metal, what happens to the voltage where the current goes to zero...


 * becomes a larger, negative number **

becomes a smaller, negative number

is unchanged

ii) Which graph would represent an increase in the intensity? Graph E iii) Which graph would represent an increase in wavelength to 290nm? Graph C iv) Which graph would represent an increase in wavelength to 500 nm? Graph I v) Which graph would represent a switch to sodium? Graph G vi) What change or combination of changes would you need to explain the change observed in Graph H above? (check all that apply)

decrease in wavelength


 * increase in wavelength **

decrease in intensity


 * increase in intensity **

7. If you have the experiment set up so that electrons are being emitted from the metal plate, which of the following are true and which are false? True True False False
 * 1) As long as conditions do not change, all emitted electrons have the same initial kinetic energy.
 * 1) The work function for the metal is different for different electrons.
 * 1) The energy of the photons hitting the plate must be less than the work function of the metal.
 * 1) The electrons emitted with the largest initial kinetic energy are those that were the least tightly bound in the metal

8. You have a colored spot light, but you don't know its precise wavelength. To find out the wavelength you shine your light on a sodium target placed in a circuit as shown in the simulation. You look up the work function of sodium and find that it is 2.3 eV. If you set the battery voltage to -0.5 V, you find that the most energetic electrons nearly reach the right plate, but turn around just before they get there. What is the wavelength, in nm, of the colored light that you used? (You can answer this question either by doing a calculation or by using the simulation. To get practice for answering the next question, we recommend that you use both methods and check that they give the same answer.) SHOW YOUR WORK/EVIDENCE.

eVs=KEmax = hf - Ψ e(0.5) =(6.626 x 10-34 * 3x108 )/(1.6 x10-19 *λ )- 4.07 2.8 = 1.24 x 10-6/λ 4.437 x 10-7 m = λ

This worked in the simulation with a wavelength of 444 nm

9. You have a plate of metal, but you have no idea what kind of metal it is. You come up with the brilliant idea of measuring the work function of this metal by using it as the target in a photoelectric effect experiment. You can perform this experiment virtually by selecting '???' as the target in the simulation. SHOW YOUR WORK/EVIDENCE.
 * 1) What is the work function, in eV, of the mystery metal?
 * 2) What is the mystery material?

With the simulation, 0.45 V was the stopping potential for 299 nm. eVs=KEmax = hf - Ψ e(0.45) =(6.626 x 10-34 * 3x108 )/(1.6 x10-19 *299 x10-9)- Ψ e(0.45) = 4.155 - Ψ 3.7eV= Ψ

The mystery metal appears to be Magnesium. It has the work function (3.68eV) that is closest to the calculated work function (3.7eV).

=Part 3=

10.Stars vary in color. Which color indicates the hottest surface temperature of a star? 11.Which of the following ojbects, all moving at the same speed, would have a de Broglie wavelength associated with them that would be larger than that of a proton travelling a the same speed? 12.When green light shines upon a given metal, it emits phtoelectrons. Which of the following will also produce photoelectric emission, using this same metal? 13.Ultraviolet light shines upon a sheet of zinc metal, and photoelectrons are emitted. If the intensity of the light is increased, 14.Consider the following frequencies of electromagnetic radiation. Which photon has the greatest energy? 15.Compared to a photon of blue light, a photon of red light has 16.An electron is confined to a box of sides L and it has a definite speed. If the walls of the box were to move inward so that the box shrinks, the electron 17.The idea of packets or quanta of energy originated with 18.A matter wave 19.Which of the following does not demonstrate the wave nature of matter? 20.When doing the photoelectric effect experiment, The wavelength of the light that strikes the metal and the work function of the metal. The intensity of the light that strikes the metal.
 * 1) The line on the graph of current to intensity can be described as linear and positive.
 * 2) The line on the graph of energy to frequency can be described as Planck's Constant.
 * 3) At a __frequency below__ the frequency required to overcome the work function, increasing the light intensity causes the current to //increase / decrease / **remain the same.**//
 * 4) At a __frequency above__ the frequency required to overcome the work function, increasing the light intensity causes the current to //**increase** / decrease / remain the same.//
 * 5) Old darkrooms (for developing film) were once illuminated with a feint red light (765nm). If this was the limit of the silver compound used in the film, solve for the work function of the silver compound. __1.62 eV____J__
 * 6) __ Consider the following scenario: On a partly cloudy day you find that a household photovoltaic array outputs 2.4 amps of current. If the clouds part and the sun comes out, exactly doubling the amount of light incident on the PV array, we should expect the array to output //2.4 A / 4.8 A / more than 4.8 A / less than 2.4 A / **between 2.4 and 4.8 A**//**.** __
 * 7) __ The work function for cesium is 1.96 eV. Find the cutoff wavelength for the metal. __ 633nm
 * 8) What is the maximum kinetic energy for the emitted electrons when 425 nm light is incident on #7’s metal? 4.67E-19J
 * 9) In certain metal, the stopping potential is found to be 3.70 V. When 235 nm light is incident on the metal, electrons are emitted. What is the maximum kinetic energy given to the electrons in eV and J? __5.28eV__ 8.448E-19J
 * 1) Red
 * 2) Orange
 * 3) Yellow
 * 4) ** Blue **
 * 1) ** An electron **
 * 2) A neutron
 * 3) A bacteria
 * 4) A baseball
 * 1) ** Low intensity blue light **
 * 2) Low intensity red light
 * 3) High intensity red light
 * 4) high intensity yellow light
 * 1) The electrons will have less energy.
 * 2) The electrons will have more energy
 * 3) ** More electrons will be emitted **
 * 4) Fewer electrons will be emitted.
 * 1) 6.6 x 10-34 Hz
 * 2) 6.6 x 10-4 Hz
 * 3) 6.6 x 104 Hz
 * 4) ** 6.6 x 1018 Hz **
 * 1) More energy
 * 2) ** Less energy **
 * 3) Shorter wavelength
 * 4) The same wavelength
 * 1) Would speed up
 * 2) Would slow down
 * 3) ** Would move with the same speed **
 * 4) Would exhibit none of the above.
 * 1) Louis de Broglie
 * 2) ** Max Planck **
 * 3) Werner Heisenberg
 * 4) Erwin Schrodinger
 * 1) Applies only to “massless” particles
 * 2) Applies only to a photon
 * 3) ** Has a wavelength inversely related to its momentum **
 * 4) Has a wavelength directly related to its momentum
 * 1) ** The cloud model of the electron **
 * 2) The two slit interference pattern
 * 3) An electron in motion in a conducting wire (circuits)
 * 4) Electron diffraction
 * 1) What determines the amount of kinetic energy photoelectrons will have?
 * 1) What determines the number of photoelectrons emitted from a metal?