Question 1

Cosmology: Dark energy accounts for what percent of the known energy in the universe?

Accepted Answer

Dark energy is estimated to account for about 68% of the total energy in the universe, according to current cosmological models. This mysterious form of energy is thought to be responsible for the accelerated expansion of the universe.

Question 2

Cosmology: Dark energy was discovered as astronomers studied

Accepted Answer

Dark energy was discovered through the study of the redshift of distant galaxies, which led to the realization that the expansion of the universe is accelerating.

Question 3

Conservation laws: Is the decay π⁰ → μ⁺ + v_μ allowed?

Accepted Answer

The answer of Conservation laws: Is the decay π⁰ →...

Question 4

Cosmology: Luminous (normal) matter makes up approximately what percentage of the known matter in the universe?

Accepted Answer

The answer of Cosmology: Luminous (normal) matter makes up approximately...

Question 5

Particle accelerators: A deuteron has the same charge as a proton but approximately twice the proton mass. Suppose deuterons are being accelerated in a cyclotron in an orbit of radius 75 cm at a frequency of 8.0 MHz. What magnetic field magnitude is needed? (e = 1.60 × 10^-19 C, m_proton = 1.67 × 10^-27 kg)

Accepted Answer

The frequency of the cyclotron is related to the magnetic field and the mass of the particle being accelerated by the following equation:

f = Bq/2πm

where f is the frequency, B is the magnetic field magnitude, q is the charge of the particle, and m is the mass of the particle.

For deuterons, q = 1.60 × 10^-19 C and m = 2(1.67 × 10^-27 kg) = 3.34 × 10^-27 kg. Plugging in these values along with the given frequency of 8.0 MHz (or 8.0 × 10^6 Hz) and solving for B, we get:

B = 2πmf/q = 2π(3.34 × 10^-27 kg)(8.0 × 10^6 Hz)/(1.60 × 10^-19 C) ≈ 1.1 T

Therefore, the best choice is C, with a magnetic field magnitude of 1.1 T.

Question 6

Particles: A neutral η⁰ (having mass 0.642 u) that is at rest decays into two gamma ray photons. What is the energy in MeV of each photon? (1 u = 931.5 MeV/c²)

Accepted Answer

The energy of each photon is half of the total energy released by the decay, which is calculated using E=mc^2. Given the mass of the particle is 0.642 u, and 1 u = 931.5 MeV/c^2, the total energy is 0.642 u * 931.5 MeV/u = 598 MeV. Since the particle decays into two photons, each photon has half this energy, which is 299 MeV.

Question 7

Particle accelerators: What type of particle accelerator has two large D-shaped electrodes with a small gap between them, through which an alternating potential difference accelerates the particles in a constant magnetic field?

Accepted Answer

The description matches that of a cyclotron. A linear accelerator (A) has a straight path for the particles to accelerate, and a synchrotron (C) uses alternating magnetic fields to accelerate the particles. None of the above (D) is not a correct choice as there is a correct answer within the options given.

Question 8

Cosmology: If the density of the universe is less than the critical density, then the total energy of the universe is

Accepted Answer

If the density of the universe is less than the critical density, then the universe is said to be "open" and its total energy is positive. This means that the amount of matter and energy in the universe is not enough to stop its expansion and it will continue to expand forever. As the universe expands, it will become less dense and less energetic.

Question 9

Conservation laws: Which one of the following processes CANNOT occur?

Accepted Answer

The answer of Conservation laws: Which one of the following...

Question 10

Conservation laws: Which one of the following decays CAN occur?

Accepted Answer

The answer of Conservation laws: Which one of the following...

Question 11

Cosmology: How long after the Big Bang did nucleosynthesis, the combining of protons and neutrons together to form nuclei, begin to occur?

Accepted Answer

Nucleosynthesis occurred roughly 3 minutes after the Big Bang, when the temperature cooled enough to allow for the formation of stable atomic nuclei.

Question 12

Cosmology: The universe first became transparent to most light, coinciding with the origin of the cosmic background radiation, when the universe cooled enough to allow the formation of

Accepted Answer

The universe first became transparent to most light when it was about 380,000 years old, which coincides with the origin of the cosmic microwave background radiation. At this time, the temperature of the universe had cooled enough to allow the formation of neutral atoms from protons and electrons. This allowed light to travel freely through space instead of being scattered by free electrons, making the universe transparent. The formation of atomic nuclei occurred earlier, within the first few minutes after the Big Bang. The formation of protons and neutrons was also an early process in the universe's history. The formation of stars and galaxies occurred much later, after the universe had expanded and cooled further.

Question 13

Particle accelerators: A cyclotron is designed with a magnet that produces a magnetic field of 1.2 T. When refurbished, the magnet is replaced by one that produces a 1.5-T field. How does the maximum kinetic energy achieved by the protons change compared to their previous maximum kinetic energy?

Accepted Answer

The maximum kinetic energy of the protons in a cyclotron is given by the equation:

K_max = qV_maxr

where q is the charge of the particle, V_max is the maximum potential difference applied to the dees, and r is the radius of the dees. The maximum potential difference in a cyclotron is given by:

V_max = Bf r^2 / (2m)

where B is the magnetic field strength, f is the frequency of the alternating voltage applied to the dees, and m is the mass of the particle.

Since the radius of the dees and the frequency of the alternating voltage remain constant, we can see that the maximum kinetic energy is proportional to the magnetic field strength. Therefore, increasing the magnetic field strength from 1.2 T to 1.5 T will increase the maximum kinetic energy by:

(K_max,new - K_max,old) / K_max,old x 100%
= [(1.5 / 1.2)^2 - 1] x 100%
= 56.25%

Therefore, the maximum kinetic energy achieved by the protons increases by 56%. The correct answer is C).

Question 14

Particle accelerators: A cyclotron of radius 0.25 m accelerates protons in a 1.7-T magnetic field. What is the frequency for the applied alternating voltage? (m_proton = 1.67 × 10^-27 kg, e = 1.60 × 10^-19C)

Accepted Answer

The cyclotron frequency is given by the formula f = (qB)/(2πm). Substituting the given values, f = (1.60 × 10^-19 C * 1.7 T) / (2π * 1.67 × 10^-27 kg) ≈ 26 MHz.

Question 15

Particles: Suppose you were to try to create a proton-antiproton pair by annihilation of two very high-energy gamma rays of the same wavelength heading toward each other. The proton and the anti-proton have the same masses, but opposite charges. What would be the minimum energy needed for each photon? (e = 1.60 × 10^-19 C, m_proton = 1.67 × 10^-27 kg, c = 3.00 × 10⁸ m/s)

Accepted Answer

The minimum energy needed for each photon to create a proton-antiproton pair is determined by the rest mass energy of the proton (or antiproton), which is given by the equation E=mc^2. The rest mass of a proton is 1.67 × 10^-27 kg, and the speed of light (c) is 3.00 × 10^8 m/s. Plugging these values into the equation gives E = (1.67 × 10^-27 kg)(3.00 × 10^8 m/s)^2 = 1.503 × 10^-10 J. Converting this energy to MeV (1 J = 6.242 × 10^12 MeV), we get approximately 939 MeV. Therefore, each photon must have a minimum energy of 939 MeV to create a proton-antiproton pair.

Question 16

Cosmology: The cosmic background radiation corresponds to a temperature of about

Accepted Answer

The cosmic background radiation corresponds to a temperature of about 2.7 K. This is a relatively low temperature, resulting from the cooling of the universe since the Big Bang. It was first detected in 1964 by Arno Penzias and Robert Wilson, and has since been studied extensively as a means of understanding the early universe.

Question 17

Conservation laws: Is the decay Σ⁺ → p + π⁺allowed?

Accepted Answer

Charge is not conserved in this decay because the initial state has a total charge of +1 (ΣS1U1P1) while the final state has a total charge of 0 (p + πS1U1P1 + S1S1P0S1U1B1 + S1U1B0). Therefore, the decay violates conservation of charge and is not allowed.

Question 18

Particle accelerators: The voltage across the dees of a cyclotron is 30,000 V. How many revolutions do the protons go through in reaching a kinetic energy of 21 MeV? (1 eV = 1.60 × 10^-19 J, e = 1.60 × 10^-19 C, m_proton = 1.67 × 10^-27 kg)

Accepted Answer

Each time a proton completes a revolution in the cyclotron, it is accelerated by the voltage across the dees, gaining kinetic energy equal to the charge of the proton times the voltage (eV). To find the total number of revolutions to reach 21 MeV, divide the total desired kinetic energy (21 MeV) by the energy gained per revolution (30,000 V or 30 keV, since 1eV = 1.60 × 10^-19 J and the charge of a proton e = 1.60 × 10^-19 C). Thus, 21 MeV / 30 keV = 700,000 keV / 30 keV = 700 revolutions.

Question 19

Particle accelerators: A cyclotron of radius 0.25 m accelerates nonrelativistic protons in a 1.7-T magnetic field. What is the kinetic energy of the protons when they leave the cyclotron? (1 eV = 1.60 × 10^-19 J, e = 1.60 × 10^-19 C, m_proton = 1.67 × 10^-27 kg)

Accepted Answer

The cyclotron equation is given by:
$$\frac{qB}{m}r=\frac{mv^2}{r}$$
where $q$ is the charge of the particle (in this case, a proton), $B$ is the magnetic field strength, $m$ is the mass of the particle, $r$ is the radius of the cyclotron, and $v$ is the speed of the particle.
Solving for $v$, we get:
$$v=\sqrt{\frac{qBr^2}{m}}$$
The kinetic energy of a particle is given by:
$$K=\frac{1}{2}mv^2$$
Substituting the expression for $v$ and solving for $K$, we get:
$$K=\frac{1}{2}m\left(\frac{qBr^2}{m}ight)=\frac{q^2B^2r^2}{2m}$$
Substituting the given values and noting that $q=e$, we get:
$$K=\frac{(1.60 	imes 10^{-19}	ext{ C})^2 (1.7	ext{ T})^2 (0.25	ext{ m})^2}{2(1.67 	imes 10^{-27}	ext{ kg})}=8.7	ext{ MeV}$$
Therefore, the answer is E: 8.7 MeV.

Question 20

Cosmology: Dark matter was initially proposed to explain

Accepted Answer

Dark matter was initially proposed to explain the velocities of stars and gases in spiral galaxy arms, which could not be accounted for by visible matter alone.

Quiz 35: Interference