Lab 8: Quantum & Atomic Physics

Lab 8: Quantum & Atomic Physics

1. Introduction

Many biological processes are triggered by

electromagnetic radiation at different frequencies. For

plants, why does visible light have sufficient energy to

enable photosynthesis while infrared light does not? How does the quantized nature of light and the

discrete energy levels of atoms enable digital imaging

detectors to function in cameras and in medical devices? These experiments will help you understand

some properties of light, both in terms of thermal

emission from objects at different temperatures and

how packets of light energy can ionize a surface. For definitions and concepts related

to this lab, review _​Chapters 25.7-25.8, 28.2-28.4_​, _​29.1-29.4 in the Knight textbook.

Note: this lab uses simulations that may be incompatible with iPads.

2. Experiment

Activity 1 - Blackbody Spectrum

In this set of experiments, you will explore how a blackbody spectrum of an object is

affected by changes in its temperature. You will also explore the relationships between

temperature, peak wavelength, and intensity. Open the Blackbody Spectrum_​simulation

and spend a few minutes exploring the available features. After resetting the simulation

to its default initial setup, study the currently displayed spectrum of the Sun. The plot

shows the spectral power density (i.e., light intensity per unit wavelength) vs.

wavelength of light in μm (1 μm = 10 _​-6 _{m). The colors of visible light are also displayed}

at their corresponding ranges of wavelengths (~0.4-0.75 μm). On this type of plot, the

area under the curve is the total emitted power in megawatts (MW) per square meter

(m_​2​_{). Check ‘Labels’ to mark the corresponding regions of the spectrum with the type of}

radiation. (Note: the _​x_​-axis begins at 0 μm, but the simulation is limited to a wavelength

range of 0.001-3 μm, which is why ultraviolet (UV) is the shortest wavelength and

infrared (IR) is the longest wavelength displayed).

How would you describe the types of radiation emitted by the Sun? For _​deliverable 1_​,

light and describe your observations. Is there more blue light than red light? Also

identify any other types of radiation in the Sun’s spectrum, and determine the region

where most of the Sun’s energy is emitted and explain your reasoning.

Figure 1:​ blackbody (thermal) radiation simulation with default configuration

Next, locate the plot save button (camera icon) below your plot settings box to save the

curve for the Sun, then use the sliding thermometer tool on the right side to make

adjustments in the temperature _​T above and below the current setting of _​T_​Sun = 5800 K.

You can use this tool to overplot/erase curves corresponding to different _​Tvalues using

the camera/eraser tool and the legend to observe the blackbody curves simultaneously.

For _​deliverable 2_​, include a screenshot of your simulation with curves at three different

T values with peaks in the visible light range on the same plot. Also describe what

happens to the shapes and the peak values of the spectrum as you change _​T_​.

The temperature of other stars varies with the type and current evolutionary stage of the

star’s life. For example, adjust _​Tto the ‘Sirius A’ setting and use the zoom settings near

the plot until you can see the entire blackbody curve. While making these changes,

also notice the B/G/R channels change in relative brightness with _​T_​; the star icon above

the plot is the overall color of a star at this _​T_​. What region of the spectrum contains the

peak power? Would you be able to see light at this wavelength? Consider

observations of the spectrum from two other stars: Star 1 has the peak power occurring

the threshold between visible red and IR. For _​deliverable 3_​, find the approximate

surface _​T of both stars (_​T_​1 and_​T_​2​) in K, and include screenshots for both. Which star is

hotter and which star is emitting more energy overall, and how do you know? Check

‘Intensity’ to get the total radiated power measurements in W/m_​2​_.

Figure 2: ​ex. blackbody curves with overplot & trace enabled

You should find that the thermal emission spectrum of a blackbody is very sensitive to

even small changes in _​T_​. The theoretical dependence of the peak wavelength 𝛌​p is

given by _​Wien’s Law_​:

λ

=

Equation 1 gives 𝛌​p in nm (1 nm = 10 _​-9 _{m) for ​T in Kelvin K. Incandescent light bulbs}

operate at a slightly lower temperature than Star 2, around 2500 °C or about 2800 K.

For _​deliverable 4_​, show your calculations using Equation 1 to predict 𝛌​pfor _​T_​L= 2800 K,

then test your prediction using the simulation. You can check ‘Graph Values’ in the

options window to enable you to trace your light bulb emission curve (e.g., Figure 2).

Use your results to explain why incandescent bulbs get hot and why they waste a lot of

energy. Evaluate your earlier measurements for Stars 1 & 2 using Equation 1 as well.

These experiments analyzed the collective distribution of energies in thermal radiation.

The next activity will focus on a famous experiment that revealed the individual energies

Activity 2 - The Photoelectric Effect

Light is an electromagnetic wave that exhibits wave-like behavior (e.g., interference,

diffraction), but light can also exhibit particle-like behavior. This set of experiments

explores Einstein’s photoelectric effect, which helps us understand the quantized nature

of light as _​photons_​. When light shines on the surface of a metal, it may eject electrons

from the metal that carry away kinetic energy (KE). We can explore what controls this

phenomenon using a reproduction of a device used to study the photoelectric effect in

the following _​simulation_​, also shown in Figure 3 below. You can also compare this

simulation with Figure 28.6 in your textbook.

Figure 3:_​ photoelectric effect simulation + target/graph controls

The setup consists of two metal plates in a vacuum connected to a source of potential

difference Δ_​V to make a complete circuit. The left plate (cathode) is the target metal

that you can expose to different wavelengths _𝛌 (or frequencies _​f_​) of light. If the light

source can eject electrons _​e_​-_{from the metal, those electrons will move towards the right}

plate (anode) and contribute to a current _​I that can be measured by the ammeter in

Amps (A). The battery is the source of Δ _​V in Volts (V) and can be adjusted to “stop” the

current or reduce it to zero. The required Δ _​V_​S to stop all current is equivalent to the

maximum KE (KE_​m​) of the ejected electrons. Using energy conservation and the

definition of electric potential, you can show that Δ V_{​ ​S} = -KE_​m​/_​q, where_{​ ​}q = -_​e = -1.6 ✕

10_​-19​ _{C is the charge on the electron and KE​m}

​

is in Joules (J) to give Δ_​V_​S​ in V.

Your first experiment will explore how light intensity affects Δ_​V_​S (and KE_​m​). If needed,

menu at the top of the simulation window, select ‘Show photons’ and use the simulation

to complete the Table 1 below. (Hint: what sign of Δ _​V_​S is needed to stop electrons from

reaching the anode and registering _​I_​ > 0?)

Table 1: Na Stopping Voltage vs. Intensity

Target 𝛌 (nm) Intensity(%) I_​(A) at Δ_​V_​​= 0 Δ_​V_​s​ (V) KE_​m​ (J)

Sodium 400 50

Sodium 400 75

Sodium 400 100

For _​deliverable 5_​, include your completed Table 1. Try to determine Δ _​V_​S to within 0.01

V such that ejected electrons stop just short of the anode plate. When close, you can

adjust Δ_​V in increments of ~0.01 V by typing values directly into the value box. Explain

why _​I increased when intensity changed. (Hint: how is the number of photons coming

from the light source related to the intensity of light?) Does the light intensity have any

effect on your values of KE_​m​? What does this tell you about the energy of each photon?

How does changing 𝛌 affect your metal target? This experiment was key support for

Max Planck’s idea that light comes in discrete packets called photons and was crucial to

Albert Einstein’s mathematical description of photoemission. In the upper right controls,

check ‘Show only highest energy electrons’, set the light intensity to 100%, and

complete Table 2 below. Hint: in addition to the slider controls for 𝛌 and Δ_​V_​S​, you can

also change them to specific values by typing into the values boxes near the slider

controls. _​Determine ΔV_​S such that ejected electrons stop just short of the negative

plate_​. When getting close, try adjusting Δ_​V_​S​ in increments of ~0.01 V. Table 2: Na Stopping Voltage vs. Light Frequency

Target 𝛌 (nm) Calculated_​ f = c/_​𝛌 (Hz) Δ_​V_​S​ (V) KE_​m​ (J) Sodium 125 __________ ✕ 10_​15 Sodium 300 __________ ✕ 10_​15 Sodium 450 __________ ✕ 10_​15 Sodium 538 __________ ✕ 10_​15 Sodium 540 __________ ✕ 10_​15

For _​deliverable 6_​, include your completed Table 2, and describe what happens in the

simulation for 𝛌≥ 540 nm. Based on your knowledge of the energy level structure of the

You should have found that at 𝛌 = 540 nm no electrons were ejected. Photons have an

energy _​E_​ given by

f

E

=

h

=

h

where Planck’s constant _​h _​= 6.63 ✕10-34_{​ J·s and the speed of light in vacuum ​c = 3.00}

✕ 10_​8 _{m/s. Those photons that just barely eject the electron have the threshold}

frequency _​f_​0​. What would you expect for _​f_​0 for your sodium metal target? In atoms,

electrons are bound to their nuclei by electrostatic forces from protons, but as you have

observed, electrons can escape if given sufficient energy, which ionizes the atom. The

minimum energy required to remove an electron from an atom is called the _​work

function _​E_​0​. For_​deliverable 7_​, use your data from Table 1 and Equation 2 to show your

work calculating _​E_​0 for sodium both in units of J and in electron volts (eV). Recall that 1

eV = 1.6 ✕ 10_​-19 _{J. For ​deliverable 8​, use your data from Table 2 to make a graph of}

KE_​m vs. _​f using Google Sheets/Excel. Be sure to clearly label your axes, and give your

values for your xy-intercepts and the slope of your best-fit line. What does the slope of

your graph represent? What do the intercepts represent?

Photoemission is the process of an electron being ejected due to the absorption of a

photon with frequency _​f > _​f_​0​, which you calculated above. Any extra energy that the

electron has exceeding _​E_​0 is given to the electron as excess KE. The value of KE _​m is

achieved when the outermost electron (i.e., the weakest binding energy) having the

smallest E_{​ ​0} is ejected. For _​deliverable 9_​, write an equation of the form _​y=_{​ ​}mx + b that

describes the best-fit line that you fit to your graph of KE _​m vs. _​fabove and describe the

meaning of each term in your equation.

Next, use the simulation to complete Table 3 below and add this new set of KE _​m vs. _​f

data to your graph for sodium above. For _​deliverable 10_​, include your completed Table

3 and your new plot with each line labeled appropriately. What is your value of slope? Table 3: Ca Stopping Voltage vs. Light Frequency

Target 𝛌 (nm) Calculated_​ f = c/_​𝛌 (Hz) Δ_​V_​S​ (V) KE_​m​ (J) Calcium 150 __________ ✕ 10_​15 Calcium 250 __________ ✕ 10_​15 Calcium 350 __________ ✕ 10_​15 Calcium 415 __________ ✕ 10_​15 Calcium 428 __________ ✕ 10_​15

By finding similarities to the Bohr model of the energy level structure in atoms, give an

explanation for why your plot indicates a different value for _​f_​0​ in sodium vs. calcium.

3. Deliverables

For full credit please include the following in your lab report. Follow the template

provided on the Weebly Lab 8 page and include one deliverable per Google Slide in the

order that they are presented for your set of activities below. Always label your images.

1. Compare the Sun’s spectrum to visible light. Is there more blue light than red

light? Identify any other types of radiation in the Sun’s spectrum, and determine

the region where most of the Sun’s energy is emitted; explain your reasoning.

2. A simulation screenshot with curves at three _​T values with peaks in visible light.

Describe what happens to the curve shapes & peak values as you change _​T_​.

3. Find the approximate _​T_​1 and _​T_​2 in K, and include screenshots for both. Which

star is hotter and which star is emitting more energy overall, and how do you

know? Give your total radiated power measurements in W/m_​2​_.

4. Calculations using Equation 1 to predict _𝛌​p​; test your prediction using the

simulation. Use your results to explain why incandescent bulbs get hot and why

they waste energy. Evaluate your earlier measurements for Stars 1 & 2.

5. Your completed Table 1. Explain why _​I increased when the intensity of light

changed. Does the light intensity have any effect on your values of KE _​m​? What

does this tell you about the energy of each photon?

6. Your completed Table 2. Describe what happens to when 𝛌≥ 540 nm. Propose

an explanation for this observation based on the energy-level structure of an

atom.

7. Use your data from Table 1 and Equation 2 to show your work calculating _​E_​0for

sodium both in units of J and in electron volts (eV).

8. Use Table 2 to a plot of KE _​m vs. _​f_​. Clearly label your axes, and give your values

for your xy-intercepts and the slope of your best-fit line. What does the slope of

your graph represent?

9. Write an equation of the form _​y _​= _​mx + b that describes the best-fit line that you

fit to your graph of KE_​m​ vs. _​f_​ above, including descriptions of each term.

10.Your completed Table 3 and updated plot. What is your value of slope? By

finding similarities to the Bohr model of the energy level structure in atoms, give

an explanation for why your plot indicates a different value for _​f_​0 in sodium vs.