## Activity: de Broglie wavelength after freefall

Contemporary Challenges 2022 (4 years)
In this activity students combine energy conservation with the relationship between the de Broglie wavelength and momentum to find the wavelength of atoms that have been dropped a given distance.

This activity follows Interference and quantum weirdness and requires at minimum the end of the lecture which discusses this experiment.

In Interference and quantum weirdness you learned about an experiment in which rubidium atoms are dropped from a trap into an optical two-slit experiment. During this experiment the atoms fall a total of 1.5 meters. What is the de Broglie wavelength of an atom after falling from rest 1.5 m? \begin{align} \lambda &= \frac{2\pi\hbar}{p} \end{align}

• assignment One-dimensional gas

assignment Homework

##### One-dimensional gas
Ideal gas Entropy Tempurature Thermal and Statistical Physics 2020 Consider an ideal gas of $N$ particles, each of mass $M$, confined to a one-dimensional line of length $L$. The particles have spin zero (so you can ignore spin) and do not interact with one another. Find the entropy at temperature $T$. You may assume that the temperature is high enough that $k_B T$ is much greater than the ground state energy of one particle.
• assignment Surface temperature of the Earth

assignment Homework

##### Surface temperature of the Earth
Temperature Radiation Thermal and Statistical Physics 2020 Calculate the temperature of the surface of the Earth on the assumption that as a black body in thermal equilibrium it reradiates as much thermal radiation as it receives from the Sun. Assume also that the surface of the Earth is a constant temperature over the day-night cycle. Use the sun's surface temperature $T_{\odot}=5800\text{K}$; and the sun's radius $R_{\odot}=7\times 10^{10}\text{cm}$; and the Earth-Sun distance of $1.5\times 10^{13}\text{cm}$.
• assignment Spin Fermi Estimate

assignment Homework

##### Spin Fermi Estimate
Quantum Fundamentals 2022 The following two problems ask you to make Fermi estimates. In a good Fermi estimate, you start from basic scientific facts you already know or quantities that you can reasonably estimate based on your life experiences and then reason your way to estimate a quantity that you would not be able guess. You may look up useful conversion factors or constants. Use words, pictures, and equations to explain your reasoning:
1. Imagine that you send a pea-sized bead of silver through a Stern-Gerlach device oriented to measure the z-component of intrinsic spin. Estimate the total z-component of the intrinsic spin of the ball you would measure in the HIGHLY improbable case that every atom is spin up.
2. Protons, neutrons, and electrons are all spin-1/2 particles. Give a (very crude) order of magnitude estimate of the number of these particles in your body.
• assignment Derivatives from Data (NIST)

assignment Homework

##### Derivatives from Data (NIST)
Energy and Entropy 2021 (2 years) Use the NIST web site “Thermophysical Properties of Fluid Systems” to answer the following questions. This site is an excellent resource for finding experimentally measured properties of fluids.
1. Find the partial derivatives $\left(\frac{\partial {S}}{\partial {T}}\right)_{p}$ $\left(\frac{\partial {S}}{\partial {T}}\right)_{V}$ where $p$ is the pressure, $V$ is the volume, $S$ is the entropy, and $T$ is the temperature. Please find these derivatives for one gram of methanol at one atmosphere of pressure and at room temperature.
2. Why does it take only two variables to define the state?
3. Why are the derivatives above different?
4. What do the words isobaric, isothermal, and isochoric mean?
• assignment Heat of vaporization of ice

assignment Homework

##### Heat of vaporization of ice
Vaporization Heat Thermal and Statistical Physics 2020 The pressure of water vapor over ice is 518 Pa at $-2^\circ\text{C}$. The vapor pressure of water at its triple point is 611 Pa, at 0.01$^\circ\text{C}$ (see Estimate in $\text{J mol}^{-1}$ the heat of vaporization of ice just under freezing. How does this compare with the heat of vaporization of water?
• face Wavelength of peak intensity

face Lecture

5 min.

##### Wavelength of peak intensity
Contemporary Challenges 2022 (3 years)

This very short lecture introduces Wein's displacement law.
• assignment Calculation of $\frac{dT}{dp}$ for water

assignment Homework

##### Calculation of $\frac{dT}{dp}$ for water
Clausius-Clapeyron Thermal and Statistical Physics 2020 Calculate based on the Clausius-Clapeyron equation the value of $\frac{dT}{dp}$ near $p=1\text{atm}$ for the liquid-vapor equilibrium of water. The heat of vaporization at $100^\circ\text{C}$ is $2260\text{ J g}^{-1}$. Express the result in kelvin/atm.
• computer Blackbody PhET

computer Computer Simulation

30 min.

##### Blackbody PhET
Contemporary Challenges 2022 (4 years)

Students use a PhET to explore properties of the Planck distribution.
• group Optical depth of atmosphere

group Small Group Activity

30 min.

##### Optical depth of atmosphere
Contemporary Challenges 2022 (4 years) In this activity students estimate the optical depth of the atmosphere at the infrared wavelength where carbon dioxide has peak absorption.
• assignment Cross Triangle

assignment Homework

##### Cross Triangle
Static Fields 2022 (5 years)

Use the cross product to find the components of the unit vector $\mathbf{\boldsymbol{\hat n}}$ perpendicular to the plane shown in the figure below, i.e.  the plane joining the points $\{(1,0,0),(0,1,0),(0,0,1)\}$.

Learning Outcomes