PHY 3106, Fall 2019, Homework #4

due Thursday, Sep. 26, at 9:30 am (beginning of class)

1.) A n* pion is a positively-charged member of the particle zoo composed of an up quark

(charge +2/3) and an anti-matter down quark (charge +1/3). It has a mass of m =

139.570 -2 .

Mey. In the rest frame of the kaon, the mean lifetime is t = 26.033 x

A) One of our upcoming experiments at Jefferson Lab will measure pions with momenta of

1.85 GeV/c. What is the total energy of the pions? B) What is the relativistic y-factor? C)

What is the kinetic energy? D) Find the velocity of the pions divided by the speed of light,

u/c.

2.) A beryllium nucleus fissions into two a-particles or helium nuclei. [The mass of beryllium is

8.0031 1 1 u, where u = 1.66 x 10-2kg. The a-particle mass is 4.001506 u.] A) In the rest

frame of the beryllium nucleus, what speed will the fission fragments have? [Hint: keep 7 or

8 significant figures for this problem. You can find u as a fraction of c for the speed.] B)

How much kinetic energy is released in the fission? [I.e., what is the "Q-value"? We will

use this definition of the Q-value next term when we study nuclear physics.]

3.) A rho meson, p, has a rest mass of moc? = 775.5 MeV. It decays to a pion, * (MT =

139.6 MeV/c2), and a massless photon, y: p* - n* +y. A) Find the total energy of each

decay particle, and B) find the velocity of each decay particle.

4.) (a) Using data from Potential Energy of a System

(http://cnx.org/content/m58312/latest/#fs- id1165039443587) find the mass destroyed

when the energy in a barrel of crude oil is released. (b) Given these barrels contain 200 liters and

assuming the density of crude oil is 750kg/m', what is the ratio of mass destroyed to original

mass, Amlm ?

5.) A metal electrode is illuminated with laser light of wavelength 380 nm. Electrons are ejected

from the metal, and slowed down by an adjustable opposing electric potential. A) If the

potential difference is adjusted to 1.10 V, the current of photoelectrons is stopped completely.

What is the work function of the metal? B) The adjustable potential is now switched off.

What is the maximum wavelength light that is able to eject electrons from the metal?

6.) An X-ray photon with a wavelength of 0.0500 nm Compton scatters from a free electron

which is initially at rest. The scattered photon is detected at an angle of 90 degrees. Find a)

the initial momentum of the photon, b) the momentum of the scattered photon, and c) the

momentum of the scattered electron.

7.) Big 105.9 (WBGG) is a radio station at 105.9 on the FM dial. It broadcasts at a frequency of

105.9 MHz, and has a broadcast power of 98,400 Watts. A) What is the wavelength of these

electromagnetic radio waves? B) These waves are also considered particles, i.e., photons.

How many photons per second emanate from the broadcast antenna?