Physics 102
Homework set 11 solutions

Exercises:

Chapter 32:

2) Blue. It is higher frequency, therefore higher energy, therefore
   was emitted by an electron making a greater energy transition.

8) Spectral lines are referred to as 'atomic fingerprints' because
   each set of spectral lines corresponds to each element's unique set
   of possible electron transitions.

24) The second statement, that when many photons are observed,
    classical physics is valid, is consistent with the correspondence
    principle.  Classical physics describes the motions of 'large'
    objects and of light when there are many photons.  The fact that
    we discovered that it fails when the objects become too small or
    when there are only a few photons, does not change its success
    with larger objects.


Chapter 33:

2) Radioactive material is always a little warmer than its
   surroundings because radioactive decays give off energy.  Some of
   this energy is converted to heat.

   A more detailed picture is that, when a radioactive nucleus decays,
   it emits a particle (alpha, beta or gamma) with a lot of kinetic
   energy.  Some of the particles have collisions with other atoms in
   the sample and transfer some energy to them.  This energy gets
   shared around and raises the average kinetic energy energy
   slightly, thus increasing the temperature.

4) Alpha particles have a positive charge, beta particles have a
   negative charge.  The direction of deflection in a magnetic field
   depends on the charge of the particle.  Gamma rays are uncharged so
   they are not deflected.

16) When a nucleus emits an alpha particle, the number of protons (and
    hence the atomic number) decreases by two.  When a nucleus emits a
    beta particle (either an e+ or an e-), the number of protons
    changes by one.  Changing the number of protons changes the atomic
    number and hence changes it to a different element.

18) Chemical properties depend on the number of electrons.  The number
    of electrons (of a neutral atom) depends only on the number of
    protons (not on the number of neutrons).  Thus, different isotopes
    of the same element will have the same number of protons, hence
    the same number of electrons and the same chemical properties.

20) Inverse square means that the intensity goes as 1/r^2 (just like
    electromagnetic field intensity, light intensity, sound intensity,
    ...).  This means that at 2 m, there will be 360/4 = 90 counts per
    minute  and at 3 m there will be 360/9 = 40 cpm.

24) Radium 226/88 has 88 protons and 226 - 88 = 138 neutrons.  After
    emitting an alpha particle, it will have 88 - 2 = 86 protons and
    138 - 2 = 136 neutrons, giving it an atomic weight of 86 + 136 =
    222.  This element is Radon 222/86.

28) When phosphorus decays, it emits a positron.  This means that a
    proton beta+ decays to a neutron, a positron and a neutrino.
    Thus, the atomic number decreases from 15 to 14.  The resulting
    nucleus is an isotope of Silicon.

34) The hot springs got its warmth from radiation.  Radiation from
    radioactive elements deep in the Earth heated the rock that heated
    the water that bubbles up in the hot springs.  The water is safe,
    because the radiation that heated it is long gone and the water
    itself is not radioactive.  However, without natural
    radioactivity, your friend could not enjoy a natural hot spring.


Problems:

Chapter 33:

2) The sample activity decreased from 160 counts per minute (cpm) to
   10 cpm.  First, let's see how many half-lives this is:

       time        |       activity (cpm)
    (half lives)   | 
-------------------------------------------
       zero                160    
       1		    80
       2		    40
       3		    20
       4		    10
       5		     5

Thus, four half-lives have elapsed when the activity is reduced to 10
cpm.  Since it took 8 hours for this to happen, one half life must
by 8 hours / 4 half-lives = 2 hours per half-life.


Estimation:

The Surry nuclear power plant releases about 4*10^20 neutrinos every
second.  We are about 50 mi = 80 km from Surry.  At this distance, the
neutrinos have spread out to cover the surface of a sphere that is 80
km in radius.  The area of this sphere is 
A = 4 pi r^2 = 12 * (8*10^4 m)^2 = 8*10^10 m^2

My surface area is A = height * width = 2 m * 0.5 m = 1 m^2.   

Thus of the neutrinos leaving Surry, 1 m^2 / 8*10^10 m^2 = 10^(-11) of
them pass through my body.  Therefore 
     4*10^20 neutrinos/second * 10^(-11) = 4*10^9 neutrinos
pass through my body every second.  That's 4 Billion
neutrinos/second.  Rather a lot!

Of course, almost none of them interact with the body at all.