Question 1

Tritium (³H) is a heavy isotope of hydrogen, composed of one proton and two neutrons. Tritium decays into ³He, a light isotope of helium, composed of two protons and one neutron, through the reaction . ${ }^{3} H \rightarrow{ }^{3} H e+\bar{e}+\bar{v}$ The production of an electron and an antineutrino in this decay shows that the reaction was governed by the: A)electromagnetic force. B)gravitational force. C)strong force. D)weak force.

Accepted Answer

The production of an electron and an antineutrino in the decay of tritium indicates that the weak force is responsible for this reaction. The weak force is responsible for processes involving the decay and transformation of subatomic particles, including nuclear reactions.

Question 2

What is the range of the strong nuclear force (the maximum distance over which it acts)? A)10^-9 m (1 nm, or roughly the size of a hydrogen atom) B)infinity C)a few thousand meters, or roughly the size of Earth) D)10^-15 m (1 fm, or roughly the size of a proton)

Accepted Answer

The strong nuclear force has a very short range, only acting over distances of about 1 femtometer (10^-15 meters), which is roughly the size of a proton. Therefore, the best choice is D.

Question 3

What is the range of the strong nuclear force compared to the size of the nucleus, 10^-14 m? A)The range of the strong nuclear force is 10 times smaller than the size of an atomic nucleus. B)The range of the strong nuclear force is infinite; it has no limit. C)The range of the strong nuclear force is the same as the size of the nucleus. D)The range of the strong nuclear force is 10 times larger than the size of an atomic nucleus.

Accepted Answer

The strong nuclear force has a very short range, typically about 1 femtometer (10^-15 m), which is smaller than the size of an atomic nucleus, making it significantly shorter in range compared to the overall size of a nucleus.

Question 4

Within which time interval from the initial Big Bang do we believe all four fundamental forces of nature were united into a single force? A)t = 0 to 10^-43 second, the Planck time, when gravity "froze out" of the universe B)t = 0 to 10⁶ years, when radiation dominated the universe C)t = 0 to 10^-35 second, when the strong nuclear force "froze out" of the universe D)t = 0 to 1 second, when photons interchanged freely with electron-positron pairs

Accepted Answer

The unification of all four fundamental forces into a single force is believed to have occurred during the Planck epoch, which lasted from t = 0 to 10^-43 seconds after the Big Bang. During this time, the universe was incredibly hot and dense, and all four forces were unified. As the universe expanded and cooled, the forces separated and distinct interactions emerged. Gravity "froze out" first, followed by the strong and weak nuclear forces, leaving only the electromagnetic force.

Question 5

During the epoch of cosmic inflation, the universe expanded very rapidly. What was the effect on the temperature of the universe?
A)As the universe expanded rapidly, it cooled rapidly. Thereafter it expanded and cooled at a more moderate rate.
B)Because of the incredible speed of the expansion, there was no time for particles to exchange energy. Thus, the temperature remained constant during the expansion.
C)Because of the tremendous amount of energy available, the temperature actually rose during the expansion.
D)The temperature decreased during the expansion and then rose again to essentially the value it had initially.

Accepted Answer

The answer of During the epoch of cosmic inflation, the...

Question 6

In modern quantum physics, the Heisenberg uncertainty principle states that the more precisely you know a particle's:
A)velocity, the more certain you are of its position in space.
B)mass, the less certain you are of its size.
C)position, the more certain you are of its speed and motion.
D)position, the less certain you are of its speed and motion.

Accepted Answer

The Heisenberg uncertainty principle states that the more precisely you know a particle's position, the less certain you are of its speed and motion. This means that if you have precise knowledge of a particle's position, its speed and motion become more uncertain, and vice versa. Therefore, option D is the correct choice.

Question 7

Particle-antiparticle pairs are coming into existence all the time in the space around (and inside!) us. According to the Heisenberg uncertainty principle, the more massive the particles, the:
A)shorter the time that they can exist.
B)less precisely we know their position.
C)longer the time that they can exist.
D)more precisely we know their position.

Accepted Answer

The Heisenberg uncertainty principle states that there is a fundamental limit to how precisely we can know both the position and momentum (or energy) of a particle. This limit is proportional to Planck's constant, which means that for more massive particles, the uncertainty in momentum (or energy) is relatively larger. As a consequence, the uncertainty in time that a particle can exist (which is related to its energy) is relatively smaller for more massive particles. Therefore, particle-antiparticle pairs with larger masses can only exist for shorter periods of time before they annihilate each other.

Question 8

According to the Heisenberg uncertainly principle, can matter spontaneously come into existence without having been created from energy?
A)No, never. Matter is a form of energy, and the spontaneous creation of matter would violate conservation of energy.
B)Yes, but only for extremely short times.
C)Yes, but only if the particles created are electrically neutral.
D)Yes, but only if an equal amount of matter disappears from some other part of the universe.

Accepted Answer

The Heisenberg uncertainty principle allows for particles and antiparticles to spontaneously come into existence for extremely short times, but they must also very quickly annihilate each other, conserving both energy and charge. This is known as vacuum fluctuations.

Question 9

The mass of a proton is 1.67 × 10^-27 kg. For what maximum length of time could a proton-antiproton pair spontaneously come into existence, without violating any laws of physics such as conservation of energy? A)3.5 × 10^-25 s B)1.1 × 10^-16 s C)2.2 × 10^-16 s D)7.0 × 10^-27 s

Accepted Answer

The correct answer is A because the energy required to create a proton-antiproton pair is 2mc^2, where m is the mass of a proton. The uncertainty principle states that the energy of a particle can be uncertain by an amount ΔE for a time Δt, where ΔEΔt ≥ h/4π, where h is Planck's constant. Therefore, the maximum time for which a proton-antiproton pair could spontaneously come into existence is Δt = h/4πΔE = h/4π(2mc^2) = 3.5 × 10^-25 s.

Question 10

What is a virtual particle?
A)a collection of particles that acts like a single particle
B)any particle that has no mass and is electrically neutral
C)a particle that can never have any detectable effect whatsoever on the real universe
D)a particle that exists for such a short time interval that we cannot detect it by direct measurement

Accepted Answer

A virtual particle is a particle that exists for such a short time interval that we cannot detect it by direct measurement. They are fundamental constituents of the quantum field theory and play a role in the calculations of physical interactions between particles. However, unlike real particles, they do not exist as independent entities with a definite location and momentum.

Question 11

A particle and an antiparticle have:
A)the same mass and the same electric charge.
B)the same mass and equal electric charges of opposite sign.
C)equal masses of opposite sign and the same electric charge.
D)equal masses of opposite sign and equal charges of opposite sign.

Accepted Answer

A particle and an antiparticle have the same mass but opposite charges. Therefore, the best choice is equal masses of opposite sign and equal charges of opposite sign, which is option D.

Question 12

The constant creation and annihilation of virtual pairs of particles and antiparticles causes a slight change in the wavelengths of the hydrogen spectral lines. This effect is called the:
A)Wolf effect.
B)Rutherford shift.
C)Lamb shift.
D)Einstein effect.

Accepted Answer

This effect is known as the Lamb shift, named after Willis Lamb who first observed it in 1947. It is a small correction to the energy levels of the hydrogen atom due to the virtual particle-antiparticle pairs that briefly appear and disappear in the vacuum around the atom.

Question 13

What is the difference between the virtual electron and virtual positron created spontaneously in the vacuum and the electron-positron pair created from a high-energy gamma ray?
A)They are exactly the same.
B)The particles created by the gamma ray are real. They can last forever if they do not annihilate. The virtual particles must recombine to become part of the vacuum within a very short time. Only under very special circumstances can they become real.
C)The particles created from the vacuum are real. They can last forever if they do not annihilate. The particles created from the gamma ray must recombine within a very short time. Only under very special circumstances can they become real.
D)The virtual particles have positive and negative mass, whereas the particles created by the gamma ray have positive mass.

Accepted Answer

The virtual electron and virtual positron created spontaneously in the vacuum are not real particles and must recombine to become part of the vacuum within a very short time. On the other hand, the electron-positron pair created from a high-energy gamma ray are real particles that can last forever if they do not annihilate. Only under very special circumstances can virtual particles become real through the process of pair production, which requires a significant amount of energy input.

Question 14

Energy and mass are equivalent according to Einstein, and both can be measured in electron volts. (1 eV is the energy acquired by an electron when accelerated through 1 volt.) If the rest mass of an electron is 511 keV, what is the threshold energy of a gamma-ray photon in order that it can undergo electron pair production?
A)1.533 MeV
B)1.022 MeV
C)0 eV, because it produces a particle-antiparticle pair
D)511 keV

Accepted Answer

According to the law of conservation of energy, the energy of the gamma-ray photon must be converted into the mass of the electron-positron pair created (as well as the kinetic energy of the created particles). Therefore, the threshold energy of the gamma-ray photon must be greater than or equal to the combined rest mass energy of the electron and positron, which is 2 x 511 keV = 1.022 MeV. Therefore, choice B is the correct answer.

Question 15

Suppose the inflationary epoch lasted 10^-32 seconds. How much mass could have been created in a virtual pair during this time without violating the law of conservation of energy? A)2 × 10^-27 kg, about the mass of one hydrogen atom B)10^-19 kg C)about 1 kg D)2 × 10³⁰ kg, about the mass of the Sun

Accepted Answer

According to the Heisenberg uncertainty principle, the energy-time uncertainty relation allows for the creation of virtual particles. The energy associated with the mass of a virtual particle pair can be calculated using E=mc², and the uncertainty principle ΔEΔt ≈ ħ/2. Solving for mass, m ≈ ħ/(2c²Δt), gives approximately 10⁻¹⁹ kg for Δt = 10⁻³² seconds.

Question 16

In the present universe there is an imbalance between particles and antiparticles. How did this originate?
A)It is believed that there are slight differences in mass between matter and antimatter. Thus the inflationary epoch, which gave mass and energy to the universe, created an imbalance of particles.
B)It is believed that there are slight differences in electric charge between matter and antimatter. Thus the inflationary epoch, which gave mass and energy to the universe, created an imbalance of particles.
C)We see only a small part of the universe. The missing antimatter is elsewhere, repelled by the negative mass of normal matter early in the history of the universe.
D)This question is an unsolved mystery of present-day cosmology.

Accepted Answer

This question is an unsolved mystery in present-day cosmology. While there are theories about why there is an imbalance between particles and antiparticles, none have been proven definitively. It remains an active area of research and investigation.

Question 17

As the temperature in the early universe decreased, pair production reactions were confined to particles of smaller and smaller mass while annihilation reactions were unaffected. Why this difference?
A)Particles and antiparticles contain a certain amount of mass-energy independent of their temperature whereas the energy of a photon depends on its temperature.
B)Photons contain a certain amount of mass-energy independent of their temperature whereas the energy of particles and antiparticles depend on its temperature.
C)When particles collide, the interaction raises their temperature, but this does not happen when gamma-ray photons interact.
D)When gamma-ray photons collide, the interaction raises their temperature, but this does not happen when particles interact.

Accepted Answer

Particles and antiparticles have a rest mass that determines the minimum energy (related to temperature) required for their creation. Photons, being massless, have energies that can vary with temperature, but this doesn't affect their existence in the same way it does for massive particles.

Question 18

During the first one-ten-thousandth second (10^-4 s) of the life of the universe, antiprotons were very common. For every billion antiprotons, how many protons were there? A)an unknown number, because the early universe was opaque and we cannot see what conditions were like then B)1 billion and 1, thus producing the matter we see today C)10 billion, thus producing the dark matter we see today D)exactly 1 billion, because protons and antiprotons were created in equal numbers

Accepted Answer

During the early universe, for every billion antiprotons, there were 1 billion and 1 protons. This slight imbalance led to the matter we see today, as the antiprotons and protons annihilated each other, leaving behind the excess protons.

Question 19

What is the situation with respect to matter and antimatter in the universe today?
A)There is perfect symmetry and balance between matter and antimatter.
B)There is a slight imbalance between matter and antimatter, with about one matter particle in excess for every billion matter-antimatter pairs.
C)There is far more matter than antimatter in the universe.
D)There is far more antimatter than matter in the universe.

Accepted Answer

The observable universe contains far more matter than antimatter. This asymmetry is a fundamental observation in cosmology, suggesting that during the early moments of the universe, conditions favored the production or survival of matter over antimatter.

Question 20

The first 380,000 years of our universe, before matter and radiation decoupled, were dominated by the primordial fireball filled with an immense quantity of radiant energy. What was the source of these photons?
A)They were created during the cosmic singularity and bounced around until the universe became transparent to radiation.
B)They were given off when the free electrons were captured by protons to form the first hydrogen atoms.
C)As the universe expanded and the radiation cooled, photons no longer had enough energy to create particles by pair production. But particles continued to annihilate and produce additional photons.
D)The "fireball" that we see in the distant past is really a reflection of all the radiation produced before that time bouncing back from the universe in its early opaque state.

Accepted Answer

As the universe expanded and cooled, photons lost energy and could no longer create particle-antiparticle pairs, but existing particles continued to annihilate, producing photons.

Quiz 26: Exploring the Early Universe

What is the range of the strong nuclear force (the maximum distance over which it acts) ?

What is the range of the strong nuclear force compared to the size of the nucleus, 10^-14 m?

Within which time interval from the initial Big Bang do we believe all four fundamental forces of nature were united into a single force?

During the epoch of cosmic inflation, the universe expanded very rapidly. What was the effect on the temperature of the universe?

In modern quantum physics, the Heisenberg uncertainty principle states that the more precisely you know a particle's:

Particle-antiparticle pairs are coming into existence all the time in the space around (and inside!) us. According to the Heisenberg uncertainty principle, the more massive the particles, the:

According to the Heisenberg uncertainly principle, can matter spontaneously come into existence without having been created from energy?

The mass of a proton is 1.67 × 10^-27 kg. For what maximum length of time could a proton-antiproton pair spontaneously come into existence, without violating any laws of physics such as conservation of energy?

What is a virtual particle?

A particle and an antiparticle have:

The constant creation and annihilation of virtual pairs of particles and antiparticles causes a slight change in the wavelengths of the hydrogen spectral lines. This effect is called the:

What is the difference between the virtual electron and virtual positron created spontaneously in the vacuum and the electron-positron pair created from a high-energy gamma ray?

Suppose the inflationary epoch lasted 10^-32 seconds. How much mass could have been created in a virtual pair during this time without violating the law of conservation of energy?

In the present universe there is an imbalance between particles and antiparticles. How did this originate?

As the temperature in the early universe decreased, pair production reactions were confined to particles of smaller and smaller mass while annihilation reactions were unaffected. Why this difference?

During the first one-ten-thousandth second (10^-4 s) of the life of the universe, antiprotons were very common. For every billion antiprotons, how many protons were there?

What is the situation with respect to matter and antimatter in the universe today?

The first 380,000 years of our universe, before matter and radiation decoupled, were dominated by the primordial fireball filled with an immense quantity of radiant energy. What was the source of these photons?