Study Guide

Modern Physics Themes

  • Space

    The Solar Neutrino Problem

    Time to dive deep into the mysterious world of the neutrino. The exits are at the front and back of the vehicle. Please keep your hands inside the vehicle and no flash photography.

    Neutrinos belong to a family of particles called leptons. The weak nuclear force and gravity both affect leptons. The charged leptons electrons (e), muons (μ), and taus (τ) also obey the electromagnetic force, but we're not concerned about them right now. Each charged lepton has a counterpart called the neutrino, which are as neutral as they come. There are three neutrino flavors, each corresponds to a kind of leptons: the electron-neutrino (νe), the muon-neutrino (νμ), and the tau-neutrino (ντ).

    Before we get ahead of ourselves, let's warm up to the subject through the annals of history.

    In the 1920's, nuclear physicists were, to put it simply, flabbergasted.

    The physicists of the 1920s thought beta decay was the result of a neutron turning into a proton. When a neutron turns into a proton, because of charge conservation, an electron had to be ejected at the same time. That part is still true.

    What left physicists with jaws gaping was the decay's energy spectrum…it wasn't what anyone expected. If one particle was to be emitted, then it should escape with a discrete spike of energy. This energy was M.I.A. And let's remember about the whole "conservation of energy" thing, it's kind of a big deal.

    Let's take a look at the observed and expected electron energies:

    Did the laws of energy conservation not apply to β-decay, as Niels Bohr claimed in 1932?

    Against reason, was that one little electron keeping the energy all to itself? Or, perhaps, was the electron sharing its energy with another particle, as Wolfgang Pauli then suggested in 1933? This would explain why the spectrum was continuous and not discrete. In essence, this is what Pauli thought:

    np + e- + ?

    The p, n, and e are the proton, neutron and electron, while the question mark represents the mysterious energy-stealing particle. The particle had to be neutral because of charge conservation, so Pauli named it the neutrino. "Neutrino" is Italian for means "little neutral one."

    In 1956, Messiers Cowen and Reines decided to verify the existence of this postulated particle. It was so small—even smaller than an electron, and worse, neutral—that it couldn't be measured directly. So they devised an experiment where a by-product would infer the production of a neutrino or anti-neutrino.

    Cowen and Reines devised a tank in which anti-neutrinos interact with water, a particle reaction that creates a neutron and a positron. This positron ends up colliding with an electron, producing two gamma-rays through matter annihilation. So if an observer measures two gamma-rays of 0.511 MeV, then by default he knows an anti-neutrino collided with water. The statistical probability for any other type of event is so low nothing else could've produced these energy lines. So yeah, that proved that the neutrino and anti-neutrino exist.

    In β-decay, an electron-flavored neutrino νe is released with a β particle, an electron. The three flavors of neutrinos, each associated with their own particles, were discovered at different times.

    In 1962, Leon Lederman and his co-workers detected the muon-neutrino νμ as a partner or counterpart to the μ particle. Finally, the tau-neutrino ντ was detected in the year 2000.

    So here's the deal. Nuclear fusion, while powering the Sun, emits tons of electron-neutrinos νe. While physicist knew that theoretically, they wanted to establish it experimentally. However, in the late 1960's, a few experiments showed there weren't as many electron neutrinos coming from the Sun as predicted. One particular experiment called the Davis experiment took place in the Homestake Goldmine in Lead, South Dakota.

    Two astrophysicists were in charge of the experiment there: John N. Bahcall and Raymond Davis Jr. Bahcall calculated the expected neutrino flux based on the Standard Solar Model while Davis designed a detector to verify this flux.

    Since neutrinos are so small and difficult to detect, the scale of the experiment was designed to be monstrously huge. Additionally, the neutrino detector was placed underground to shield it from other solar radiation sources. A large tank was filled with 100,000 gallons of a cleaning fluid rich in chlorine. When a neutrino collides with a chlorine atom, chlorine decays into argon. It was the level of argon that was measured in the end and compared to Bahcall's calculations.

    And then, horror of horrors: the numbers didn't match.

    It wasn't even a small discrepancy—it was huge. About two thirds of electron neutrinos were missing. The experiment was repeated several times with the same results. This came to be known as the solar neutrino problem.

    The problem was solved in 2001 by our good old friendly neighbors to the North at the Subdury Neutrino Observatory in Ontario, Canada. It turns out these little tricky neutrinos were oscillating between their electron, muon, and tau flavors within the laws of quantum mechanics. Davis' experiment could only detect electron-neutrinos: a third of the neutrinos. That's why the numbers were off.

    We still don't completely understand neutrinos. Their oscillations imply they have mass, we verified this experimentally in 1998. They contradict certain aspects of nuclear physics, violate a few laws and still, to this day, we don't know their exact mass nor understand their precise role in the universe, cosmology, and nuclear physics.

  • Energy

    Fusion in the Sun

    We've read about fusion in stars when discovering hydrostatic equilibrium in our Fluids module10. Let's take a closer look at what happens inside the layers of our own Sun.

    Our Sun is currently about 4.6 billion years old and weighs approximately 1.99 × 1030 kg. Its surface temperature is 5,777 K and its composition is 92.1% hydrogen and 7.8% helium11.

    A star is an ideal place for fusion. Stars are huge (we mean really, really, really big), and things with that much mass, have a ton of gravity. The sheer force of gravity in stars bring elements that would be gases on Earth so close to each other that they become liquids, which raises the temperature drastically in the interior of the sun. These high temperatures correspond to very high energy levels, enough energy to fuse two nuclei, that fusion creates a new element and releases even more energy.

    Since a helium nucleus has more nucleons, it requires more binding energy to keep it together. Binding energy is negative. This means helium has less mass per nucleon than hydrogen. This extra mass is radiated as energy, which we see as light. This is done through a process known as the proton-proton chain, P-P chain for short, which we can admire here.

    Now, we know why exactly our beautiful Sun shines away with life-giving energy.

  • Weapons

    Thermonuclear Weapons

    Fission weapons are actually not that efficient compared to the development of weapons of mass destruction after World War II. Thermonuclear weapons were built after the destruction of Hiroshima and Nagasaki. These more sophisticated weapons still use fission, but only as a heat source to induce nuclear fusion.

    H-bombs (short for hydrogen bombs) are thermonuclear weapons that use both fission and fusion in stages. The energy released in one stage provides the required energy for the next stage to occur. It's like a tragic play in two acts: Act II can't occur before Act I. Make no mistake, it is a tragedy when these bombs go off.

    Nuclear weapon testing was performed by the US in the Bikini islands of Hawaii and by Russia in the Arctic Circle. These geographic regions remain unsafe and have since remained deserted. Since radiation by-products, called radiation fall-out, can't be contained, there's no way to measure the extent of the damage that, at some level, generations of lifeforms are all exposed to.

    Interestingly enough, the Nobel Committee awarded Andrei Skharov, one of the Russian nuclear physicists that helped designed the most dangerous thermonuclear weapon in history, the Tsar Bomba, the Nobel Peace prize in 1975.

    The entire Cold War was about having weapons so terrible that no one would want to use them for fear of annihilation in retaliation. But that's for another section.

  • Background Radiation

    Primoridal Radiation

    As mentioned before, we're surrounded by natural levels of radiation. This natural level of radiation is present in all rock on Earth and is called primordial radiation.

    The most important primordials consist of three very long-lived isotopes with half-lives to the order of 109 years. Yes, you read right: 109 years or 1,000,000,000 years or 1 trillion years, so they're not going anywhere anytime soon. By "they," we mean the incredible threes: Potassium, Uranium, and Thorium, 40K, 238U, and 232Th. They live in the Earth's continental upper crust with an average concentration of , , and , respectively.

    Like all the other radiation we've studied, the three primordial buddies emit a variety of byproducts: other types of nuclei, neutrons, α-particles, β-particles, and γ-rays in a wide range of energies. Potassium-40 decays by beta radiation to the stable isotope of 40Ca, or undergoes electron capture to the stable isotope of 40Ar. However, 40K is only naturally abundant in certain rock compounds at low levels of 0.0117%.

    The other two main sources of primordial radiation are 238U and 232Th, which eventually decay to the stable isotopes 206Pb and 208Pb after a series of decays. Check out these two "simplified" schemes that show the number of decays each isotope undergoes before finally having a chance to catch its breath. In terms of an experiment, all this radiation output is called "background."

    Experimental physicists have to make sure their experiments aren't skewed by these natural levels of radiation by measuring the background radiation in the environment of the experiments, or by minimizing background radiation through thick radiation shields. Otherwise, the primordials could hide or even bury the signal of interest, depending on the strength of the signal.