PHY 132 T4 HW Solutions

Does motion affect the rate of a clock as measured by an observer moving with it? Does motion affect how an observer moving relative to a clock measures its rate?

Suppose an astronaut is moving relative to the Earth at a significant fraction of the speed of light. (a) Does he observe the rate of his clocks to have slowed? (b) What change in the rate of Earth-bound clocks does he see? (c) Does his ship seem to him to shorten? (d) What about the distance between stars that lie on lines parallel to his motion? (e) Do he and an Earth-bound observer agree on his velocity relative to the Earth?

(a) What is 𝛾 if 𝑣=0.250⁢𝑐? (b) If 𝑣=0.500⁢𝑐?

(a) What is 𝛾 if 𝑣=0.100⁢𝑐? (b) If 𝑣=0.900⁢𝑐?

Particles called 𝜋-mesons are produced by accelerator beams. If these particles travel at 2.70×10^8m/s and live 2.60×10^−8s at rest relative to an observer, how long do they live as viewed in the laboratory?

If relativistic effects are to be less than 1%, then 𝛾 must be less than 1.01. At what relative velocity is 𝛾=1.01?

A spaceship, 200 m long as seen on board, moves by the Earth at 0.970⁢𝑐. What is its length as measured by an Earth-bound observer?

How fast would a 6.0 m-long sports car have to be going past you in order for it to appear only 5.5 m long?

Suppose a spaceship heading straight towards the Earth at 0.750⁢𝑐 can shoot a canister at 0.500⁢𝑐 relative to the ship. (a) What is the velocity of the canister relative to the Earth, if it is shot directly at the Earth? (b) If it is shot directly away from the Earth?

Suppose a spaceship heading directly away from the Earth at 0.750⁢𝑐 can shoot a canister at 0.500⁢𝑐 relative to the ship. (a) What is the velocity of the canister relative to the Earth, if it is shot directly at the Earth? (b) If it is shot directly away from the Earth?

Find the momentum of a helium nucleus having a mass of 6.68×10^–27⁢kg that is moving at 0.200⁢𝑐.

What is the momentum of an electron traveling at 0.980⁢𝑐?

What is the rest energy of an electron, given its mass is 9.11×10^−31⁢kg? Give your answer in joules and MeV.

Find the rest energy in joules and MeV of a proton, given its mass is 1.67×10^−27⁢kg.

Why don’t we notice quantization in everyday events?

 Is visible light the only type of EM radiation that can cause the photoelectric effect?

The difference in energy between allowed oscillator states in HBr molecules is 0.330 eV. What is the oscillation frequency of this molecule?

What is the energy in joules and eV of a photon in a radio wave from an AM station that has a 1530-kHz broadcast frequency?

(a) Find the energy in joules and eV of photons in radio waves from an FM station that has a 90.0-MHz broadcast frequency. (b) What does this imply about the number of photons per second that the radio station must broadcast?

Do the unit conversions necessary to show that hc=1240eV⋅nm, as stated in the text.

(a) Find the momentum of a 4.00-cm-wavelength microwave photon. (b) Discuss why you expect the answer to (a) to be very small.

(a) What is the wavelength of a photon that has a momentum of 5.00×10^−29⁢kg⋅m/s?(b) Find its energy in eV.

At what velocity will an electron have a wavelength of 1.00 m?

What is the wavelength of an electron moving at 3.00% of the speed of light?

At what velocity does a proton have a 6.00-fm wavelength (about the size of a nucleus)? Assume the proton is nonrelativistic. (1 femtometer = 10^−15m.)

How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?

By calculating its wavelength, show that the first line in the Lyman series is UV radiation.

Find the wavelength of the third line in the Lyman series, and identify the type of EM radiation.

Look up the values of the quantities in 𝑎B= ℎ^2/4⁢𝜋^2⁢𝑚𝑒⁢𝑘𝑞^2𝑒, and verify that the Bohr radius 𝑎B is 0.529×10^−10m.

Verify that the ground state energy 𝐸0 is 13.6 eV by using 𝐸0=2⁢𝜋^2⁢𝑞^4𝑒⁢𝑚𝑒⁢𝑘^2/ℎ^2.

If a hydrogen atom has its electron in the 𝑛=4 state, how much energy in eV is needed to ionize it?

A hydrogen atom in an excited state can be ionized with less energy than when it is in its ground state. What is 𝑛 for a hydrogen atom if 0.850 eV of energy can ionize it?

What is the source of the energy emitted in radioactive decay? Identify an earlier conservation law, and describe how it was modified to take such processes into account.

Neutrinos are experimentally determined to have an extremely small mass. Huge numbers of neutrinos are created in a supernova at the same time as massive amounts of light are first produced. When the 1987A supernova occurred in the Large Magellanic Cloud, visible primarily in the Southern Hemisphere and some 100,000 light-years away from Earth, neutrinos from the explosion were observed at about the same time as the light from the blast. How could the relative arrival times of neutrinos and light be used to place limits on the mass of neutrinos?

Explain how a bound system can have less mass than its components. Why is this not observed classically, say for a building made of bricks?

The unified atomic mass unit is defined to be 1⁢u=1.6605×10−27kg. Verify that this amount of mass converted to energy yields 931.5 MeV. Note that you must use four-digit or better values for 𝑐 and ∣𝑞𝑒∣.

(a) Write the complete 𝛽+ decay equation for 11C.(b) Calculate the energy released in the decay. The masses of 11C and 11B are 11.011433 and 11.009305 u, respectively.

(a) Calculate BE/𝐴 for 12C. Stable and relatively tightly bound, this nuclide is most of natural carbon. (b) Calculate BE/𝐴  for 14C . Is the difference in BE/𝐴  between 12C and 14C  significant? One is stable and common, and the other is unstable and rare.