Physical constants

Boltzmann's constant k= 1.38066E-23 J/K

k= 0.00008617 eV/K

Atomic mass unit u= 1.66E-27 kg

= 931.5 MeV/c^2

Wien constant 2.90E-03

Planck's constant h= 4.14E-15 eV s

h= 6.63E-34 J s

h/ 2 pi = hbar =1.05E-34 J s

= 6.59E-16 eV s

hc =1.24E+03 eV nm

Speed of light c= 3.00E+08 m/s

Electron charge e= 1.60E-19 C

electron volt eV= 1.60E-19 joule

electron mass = 9.11E-31 kg

= 5.11E-01 MeV

proton mass = 1.67E-27 kg

= 9.38E+02 MeV

Stefan's constant= sigma= 5.67E-08 watt/m^2K^4

Nuclear distance unit fermi = 1.00E-15 m (a femtometer)

1. Many of the more massive stars get their energy from a fusion cycle
called the "carbon cycle". Assume

that the path to carbon just involves the fusion of 12 protons
to form carbon-12 (which has a mass of

exactly 12 amu). Never mind how it gets rid of the 6 units of
charge - just calculate the energy

yield from converting 12 protons to a carbon-12 nucleus.

Mass of 12 protons = 938 * 12
= 11256 MeV

Mass of carbon-12 nucleus = 12*931.5 MeV = 11178
MeV

Energy yield per carbon
78 MeV

2. The hottest experiment in high energy physics right now is the planned
collisions of gold nuclei at

Brookhaven in a ring of circumference 2.4 miles. Taking the mass of
the gold nucleus to be

197 amu and assuming it to be stripped of electrons (i.e., positive
charge +79), what magnetic field

will be necessary to accelerate the gold nuclei in this 615 meter
radius circular path. Assume the

velocity to be the speed of light - it's close enough.

F=mv^2/r = qvB, so B = mv/qr m=197*1.66E-27kg/amu = 3.2702E-25 kg

B= (3.27E-25 kg)(3E8 m/s)/(79*1.6E-19 C*615 m) =
1.26E-02 Tesla

= 126 Gauss

3. Taking Rohlf literally in his approximation that all atoms have diameters
of 0.3 nm, what density do you

get for aluminum which has an atomic mass of 27? I've alway thought
this 2.7 gm/cm3 = 2700 kg/m3

was a bit strange.

Approximate by cubic volume = cube of 0.3 nm =
2.7E-29 m^3

Mass = 27*1.66E-27 Kg = 4.482E-26 kg

Density =
m/V = 1660 k/m^3