Download brief answers - Inside Mines

Quantum Phenomena “Mastery of Fundamentals” Questions
CH351 – Prof. Wu
Here are some questions to test your mastery of the fundamentals of quantum
phenomena. Once you’ve mastered the material, you should be able to answer these
questions without reference to your notes or textbook.
1. What is a blackbody? What is observed in blackbody radiation, and why is it
surprising? What did Planck hypothesize to explain it?
A blackbody is an object that totally absorbs and emits all frequencies of light. At a
given temperature, the emission spectrum of a blackbody shows a maximum in
frequency that is proportional to the temperature. This is surprising because classical
physics predicts a spectrum that grows without bound, i.e the “ultraviolet
catastrophe”. Planck was able to theoretically reproduce the observed spectrum by
hypothesizing that the energy levels of the atoms in a blackbody are quantized.
2. What is the photoelectric effect? What is surprising and what did Einstein
propose to explain it?
The photoelectric effect occurs when light shining on a material (usually a metal)
causes electrons to be ejected. The number of electrons ejected is proportional to the
intensity, while their kinetic energy is proportional to the frequency minus a constant
that depends on the material. This is surprising because classically one expects the
energy to increase with intensity and not frequency. Einstein explained this by
proposing that light arrived as photons, i.e. quantized packets of light having energy
E = hν, where h is the same Planck’s constant that appeared in Planck’s hypothesis
explaining blackbody radiation.
3. What does the hydrogen spectrum look like? How can it be explained by a series
of discrete energy levels? What mathematical relationship describes these levels?
The H spectrum is a sequence of discrete lines. Using Einstein’s hypothesis that the
light carries energy hν, each line corresponds to a transition between two states of the
atom. The spectrum is completely explained by a set of discrete states with energies
proportional to 1/n2, with n = 1, 2, 3, ….
4. Given a line in the hydrogen spectrum, how can we determine which energy states
were involved in the transition?
Since Ephoton = hν = ΔEatom = (-R∞/ n f 2) - (-R∞/ n i 2), the frequency of the line can be
used to solve for 1/ n i 2 - 1/ n f 2. If one of these n is known (for instance the starting
state), the other state can be determined. Otherwise, it may be possible to tell by
inspection what pair of integers n f and n i will satisfy the equation.
5. What is deBroglie’s hypothesis? What experimental observations support his
hypothesis?
Quantum Phenomena “Mastery of Fundamentals” Questions
CH351 – Prof. Wu
deBroglie hypothesized that, like light, matter exhibited wave-like properties, and
these waves had a wavelength related to momentum according to λ = h/p. Direct
observations of the wave-like nature of matter include the diffraction of electrons off
a crystal (e.g. metal), diffraction of neutrons off a crystal, and the electron standing
wave patterns seen in STM (as seen in class).
6. What is the Bohr theory of hydrogen, and how is it explained by deBroglie’s
hypothesis?
Given that the hydrogen spectrum could be explained by a set of discrete energy
states, Bohr hypothesized that these states were just classical orbits of the electron
around the nucleus, but chosen such that the energies matched those necessary to give
the hydrogen spectrum. These orbits have a circumference that is an integer multiple
of the deBroglie wavelength of an electron in that orbit, providing a simpler
alternative criteria for which orbits are allowed.
7. What is the Heisenberg uncertainty principle? How do I use it?
The Heisenberg uncertainty principle, in its most common form, states that one
cannot determine the position and momentum of a particle to arbitrary accuracy
simultaneously. In particular, the product of the uncertainties in the measurement of
the position and the momentum is always greater than h /2 .
In addition, you should feel comfortable doing problems like those that have been
€
assigned in homework.