Quantum Mechanics 101 · Unit 1: The Classical World Cracks

Quantum Academy · Chapter 1: Welcome to the Lab: What Is Quantum Mechanics?

The rules of the very small — and why they run everything you can see

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Instructions. Work through these questions after the lesson and the lab. Use h = 6.626×10⁻³⁴ J·s, c = 3.00×10⁸ m/s and 1 eV = 1.602×10⁻¹⁹ J unless told otherwise. Show your working on calculation questions, give answers to two or three significant figures, and commit to an answer before you read the explanation. One point for each vocabulary match and each question; the challenge is a bonus.

Part A Vocabulary matching

Write the letter of the matching definition in the blank beside each term.

1.Quantum
2.Quantum mechanics
3.Classical physics
4.Planck's constant
5.Reduced Planck constant
6.Photon
7.Electron-volt
8.Quantization
9.Wave-particle duality
10.Superposition
11.Uncertainty principle
12.Entanglement

A.Pre-quantum physics, chiefly Newton's mechanics and Maxwell's electromagnetism, in which quantities vary smoothly and objects always have definite properties.
B.The energy an electron gains when accelerated through one volt, 1.602×10⁻¹⁹ J; the natural unit for atomic energies.
C.The fact that light and matter propagate and interfere like waves yet are always detected as localized particles.
D.A joint state of two or more particles that cannot be split into separate states for each, producing correlations no local pre-set instructions can explain.
E.The smallest discrete amount of a physical quantity that can be exchanged, such as one photon of light at a given frequency.
F.The restriction of a quantity, especially the energy of a bound or confined system, to discrete allowed values.
G.The framework of physical law that predicts the states, time evolution and measurement probabilities of matter and light; dominant at atomic scales and below.
H.A single quantum of light carrying energy hf; light is always emitted and absorbed in whole ones.
I.Heisenberg's rule that no state has both sharp position and sharp momentum: Δx·Δp ≥ ħ/2.
J.The constant h = 6.62607015×10⁻³⁴ J·s that sets the size of quantum effects and converts frequency into energy through E = hf.
K.h divided by 2π, about 1.055×10⁻³⁴ J·s, written ħ and used with angular frequency in E = ħω.
L.A quantum state formed as a weighted combination of other states, whose components can interfere with each other.

Part B Questions

1.
In physics, the word quantum most accurately means:Circle one
1. AA sudden, enormous change
2. BThe smallest discrete amount of a quantity
3. CAnything that involves atoms
4. DAn effect that occurs only when someone observes it
2.
Planck's constant has units of energy multiplied by time.Circle one
TrueFalse
3.
The reduced Planck constant is defined as ħ = h divided by .Fill in the blank
4.
Which of these would be hardest to catch showing wave-like interference in a laboratory?Circle one
1. AAn electron passing through a crystal
2. BA single photon from a laser
3. CA neutron passing through a crystal
4. DA rolling tennis ball
5.
Calculate the reduced Planck constant ħ from h = 6.626×10⁻³⁴ J·s.Show your working
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Answer:
6.
A red laser pointer emits light of wavelength 650 nm. Find the energy of one photon in joules and in electron-volts.Show your working
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Answer:
7.
The red pointer from the previous question has an output power of 5.0 mW. How many photons does it emit per second?Show your working
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Answer:
8.
A GPS receiver's clock is off by 20 ns (1 ns = 10⁻⁹ s). How large a distance error does this cause?Show your working
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Answer:
9.
A hydrogen atom is about 1.06×10⁻¹⁰ m across. How many hydrogen atoms, lined up side by side, would span 1 mm?Show your working
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Answer:
10.
In quantum mechanics, a measurement only counts if a conscious person looks at the result.Circle one
TrueFalse
11.
Why is the electron's magnetic moment famous in physics?Circle one
1. AIt was the first quantity Max Planck measured, in his 1900 study of hot objects
2. BIt shows that quantum mechanics breaks down for a single electron held in a trap
3. CMeasurement and quantum electrodynamics agree to about one part in a trillion
4. DIt changes value depending on whether a person is watching the experiment
12.
The SI second is defined by counting 9,192,631,770 cycles of the radiation from a quantum transition in atoms of .Fill in the blank
13.
Someone says: 'Quantum mechanics is just a theory nobody uses.' Write a two- or three-sentence reply that answers both halves of the claim.Short answer
14.
List the five big ideas of the course and describe any two of them in one sentence each.Short answer

Part C Mad scientist challenge bonus

When does the graininess bite? A quantum of energy hf matters when it is not tiny compared with the random thermal energy, roughly kT, that jostles everything at temperature T, where k = 1.381×10⁻²³ J/K is Boltzmann's constant. Take T = 300 K, room temperature. (a) Find the frequency f* at which hf* = kT, and the wavelength of light with that frequency. (b) Compute the ratio hf/kT for (i) green light of wavelength 532 nm, (ii) the caesium clock transition at 9,192,631,770 Hz, and (iii) the 1.00 m pendulum from the worked example, with f = 0.498 Hz. (c) Interpret each ratio.

Working

Memory aid

Mnemonic Quincy's Wild Socks Unravel Everything. The first letters give the five big ideas in order: Quantization, Wave-particle duality, Superposition, Uncertainty, Entanglement. Then attach a meaning to each with the chant Steps, Ripples, Blends, Blur, Bonds: energy comes in steps; light and matter travel as ripples but land as dots; states blend and interfere; position and momentum blur against each other; entangled particles share one bond, a single joint state. To use it, say the sentence, then tap one finger per idea while saying its chant word and a one-sentence definition. Five fingers in thirty seconds means you own the map of the course.

In one line Quantum mechanics is the rulebook of the very small: Planck's tiny constant sets its scale, and everything you can see runs on it.