Physics

The velocity of a proton (${}^1_1\mathrm{H}$) is twice the velocity of an alpha particle (${}^4_2\mathrm{He}$). The proton has a de Broglie wavelength of $\lambda$.

What is the de Broglie wavelength of the alpha particle?
A. $\frac{\lambda}{8}$
B. $\frac{\lambda}{2}$ C. D.

Jo is in the centre of a train carriage travelling close to the speed of light to the right. Lamps F and B, located at the front and back of the train respectively, are switched on simultaneously as Jo passes an observer Bo, who is on the platform equidistant from the lamps when the light is emitted.

According to Bo, which of the following statements is correct in terms of the perceived arrival times of the flashes of light?
A. The lights turn on simultaneously for Jo.
B. The lights turn on simultaneously for Bo.
C. The light at the back turns on before the light at the front for Jo.
D. The light at the front turns on before the light at the back for Bo.

Three identical atomic clocks are made so that they tick at precisely the same rate. One is kept in a laboratory, $X$, on Earth’s equator. Another is placed on board a satellite, $Y$, in a circular orbit with a period of 12 hours. A third is placed in a satellite, $Z$, that is in a geostationary orbit. The satellites orbit Earth in the equatorial plane.

Assume that the satellites are inertial frames of reference and the clocks are affected ONLY by the predictions of special relativity.

Which statement correctly compares the rates at which the clocks tick, as determined by an observer at $X$, when the satellites are in the positions shown in the diagram?
A. The clock at $Y$ ticks faster than either the clock at $X$ or the clock at $Z$.
B. The clock at $Y$ ticks slower than either the clock at $X$ or the clock at $Z$.
C. The clocks tick at different rates, with $X$ being the fastest and $Y$ being the slowest.
D. The clocks tick at different rates, with $Z$ being the slowest and $X$ being the fastest.

Muons are unstable particles produced when cosmic rays strike atoms high in the atmosphere. The muons travel downward, perpendicular to Earth’s surface, at almost the speed of light.

Classical physics predicts that these muons will decay before they have time to reach Earth’s surface.

Explain qualitatively why these muons can reach Earth’s surface, regardless of whether their motion is considered from either the muon’s frame of reference or the Earth’s frame of reference.

The simplified model below shows the reactants and products of a proton–antiproton reaction which produces three particles called pions, each having a different charge.

There are no other products in this process, which involves only the rearrangement of quarks. No electromagnetic radiation is produced. Assume that the initial kinetic energy of the proton and antiproton is negligible.

Protons consist of two up quarks ($u$) and a down quark ($d$). Antiprotons consist of two up antiquarks ($\bar{u}$) and a down antiquark ($\bar{d}$). Each of the pions consists of two quarks.

The following tables provide information about hadrons and quarks.

Table 1: Hadron information

Table 2: Quark charges

(c) Calculation of the pions’ velocities using classical physics predicts that each pion has a velocity, relative to the point at which the proton–antiproton reaction occurred, which exceeds $3 \times 10^8\ \mathrm{m\,s^{-1}}$.

Explain the problem with this prediction and how it can be resolved.

Which of the following statements is true regarding the observations of two people, one travelling at $99.9\%$ of the speed of light, and one stationary?
(A) Both people will observe time to be passing at the normal rate in their frame of reference.
(B) The person travelling at $99.9\%$ of the speed of light will observe their time to be passing slower.
(C) The stationary person will observe their time to be passing slower.
(D) Both people will observe time to be passing slower in their frame of reference.