Revolutions in Modern Physics: Test Review

Key facts

Where marks get lost

• ×Mixing up which time is proper. The proper time $\Delta t_0$ belongs to the observer who sees both events at the same place, and it is always the shorter one. If your 'dilated' time comes out smaller than the proper time, you have them reversed. (Special Relativity)
• ×Multiplying the length by $\gamma$ instead of dividing. Moving objects get shorter, so $L=L_0/\gamma$ must be less than $L_0$. (Special Relativity)
• ×Contracting the dimensions perpendicular to the motion. Only the length along the direction of travel changes. (Special Relativity)
• ×Forgetting to square the ratio: using $\sqrt{1-v/c}$ instead of $\sqrt{1-v^2/c^2}$. At $0.80c$ that gives $\gamma =2.24$ instead of the correct $1.67$. (Special Relativity)
• ×Thinking time dilation is only an illusion caused by light taking time to arrive. It remains after that delay is accounted for, and clocks brought back together really do disagree. (Special Relativity)
• ×Using $E=\gamma m{c}^2$ as the kinetic energy. That is the total energy; subtract the rest energy to get $E_k=(\gamma -1)m{c}^2$. (Mass-Energy Equivalence and Relativistic Energy)
• ×Using $\frac{1}{2}m{v}^2$ for particles moving faster than about $0.1c$. Above that speed the classical formula underestimates the kinetic energy, badly so near $c$. (Mass-Energy Equivalence and Relativistic Energy)
• ×Forgetting to convert atomic mass units or grams to kilograms before multiplying by $c^2$, or forgetting to square $c$. (Mass-Energy Equivalence and Relativistic Energy)
• ×Thinking the mass defect means a nucleus has more mass than its parts. A bound nucleus is lighter; energy must be added to separate it. (Mass-Energy Equivalence and Relativistic Energy)
• ×Saying a photon of exactly $0.511\text{MeV}$ can create an electron-positron pair. Pair production needs at least $1.02\text{MeV}$, enough for the rest energy of both particles. (Mass-Energy Equivalence and Relativistic Energy)
• ×Using Celsius in Wien's law. The temperature must be in kelvin; $37^{\circ }\text{C}$ gives an answer about eight times too large if not converted. (Blackbody Radiation and Planck's Quantum Hypothesis)
• ×Thinking that a hotter object's curve only moves left. It also rises at every wavelength, because the total power grows as $T^4$. (Blackbody Radiation and Planck's Quantum Hypothesis)
• ×Assuming the colour you see is the peak wavelength. The Sun peaks in the green-blue, yet looks white because it emits strongly across the whole visible band. (Blackbody Radiation and Planck's Quantum Hypothesis)
• ×Saying Planck proposed photons. Planck quantized the energy of the oscillators in the walls; Einstein proposed in 1905 that light itself travels in quanta. (Blackbody Radiation and Planck's Quantum Hypothesis)
• ×Believing classical theory failed everywhere. It matched the measured curves at long wavelengths and failed only toward the ultraviolet. (Blackbody Radiation and Planck's Quantum Hypothesis)
• ×Subtracting a work function in electron-volts from a photon energy in joules. Convert both to the same unit before using $E_{k,max}=hf-W$. (Photons and the Photoelectric Effect)
• ×Saying that brighter light makes the electrons faster. Intensity changes the number of electrons; only frequency changes their maximum kinetic energy. (Photons and the Photoelectric Effect)
• ×Getting a negative kinetic energy and reporting it. A negative result means the photon energy is below the work function, so no electrons are emitted at all. (Photons and the Photoelectric Effect)
• ×Forgetting to convert nanometres to metres in $E=hc/\lambda$, which makes the energy $10^9$ times too small. (Photons and the Photoelectric Effect)
• ×Mixing up the threshold frequency and the threshold wavelength: light must be above $f_0$, which means below ${\lambda }_0$. (Photons and the Photoelectric Effect)
• ×Calculating a photon's momentum with $p=mv$. A photon has no mass, so that formula does not apply; its momentum is $p=h/\lambda$. (Matter Waves and Wave-Particle Duality)
• ×Forgetting to convert grams to kilograms in $\lambda =h/(mv)$, which makes the wavelength 1000 times too large. (Matter Waves and Wave-Particle Duality)
• ×Thinking the Compton effect makes X-rays shorter in wavelength. The photon loses energy to the electron, so its wavelength gets longer. (Matter Waves and Wave-Particle Duality)
• ×Subtracting energy levels in the wrong order and getting a negative photon energy. The photon energy is the size of the gap: higher level minus lower level. (Matter Waves and Wave-Particle Duality)
• ×Believing large objects have no wavelength. They do; it is simply far too small to detect. (Matter Waves and Wave-Particle Duality)
• ×Thinking the interference pattern comes from electrons bumping into each other. The pattern still forms when electrons pass through one at a time. (The Uncertainty Principle and Probability Waves)
• ×Treating the wave function as a physical cloud of smeared-out charge. $|\psi {|}^2$ gives the probability of finding the whole particle at a place; every detection finds a complete electron. (The Uncertainty Principle and Probability Waves)
• ×Blaming the uncertainty principle on clumsy instruments. It is a property of waves and of nature itself; no better technology can beat $\Delta x\Delta p\ge h/4\pi$. (The Uncertainty Principle and Probability Waves)
• ×Forgetting to convert speed uncertainty to momentum uncertainty by multiplying by the mass, or using the speed itself instead of its uncertainty. (The Uncertainty Principle and Probability Waves)
• ×Assuming tunnelling means the particle gains enough energy to climb over the barrier. It passes through with the same energy, and the probability drops sharply as the barrier thickens. (The Uncertainty Principle and Probability Waves)
• ×Calling protons and neutrons fundamental particles. They are baryons made of quarks; only quarks, leptons and the bosons are fundamental in the Standard Model. (The Standard Model of Particle Physics)
• ×Mixing up baryons and mesons. Baryons have three quarks; mesons have a quark and an antiquark. (The Standard Model of Particle Physics)
• ×Forgetting that an antiquark has the opposite charge of its quark, so $\bar{\text{d}}$ is $+\frac{1}{3}$, not $-\frac{1}{3}$. (The Standard Model of Particle Physics)
• ×Saying that annihilation destroys energy. Mass disappears, but the energy $m{c}^2$ is carried away by the photons. (The Standard Model of Particle Physics)
• ×Listing the graviton as a confirmed Standard Model particle. It has been proposed but never detected, and gravity is not included in the Standard Model. (The Standard Model of Particle Physics)

Practice test

21 questions from across the unit. Each one shows the lesson it comes from.

Endless drill

Fresh numbers every time, for the calculation questions in this unit.