Chapter five quiz

Physical constants
Boltzmann's constant  k= 1.3807E-23 J/K
k= 0.00008617 eV/K
Atomic mass unit   u= 1.66E-27 kg
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
h/ 2 pi hbev 6.59E-16 eV s
Speed of light  c= 3.00E+08 m/s
hc= 1.24E+03 eV nm
hbarc= 1.97E+02 eV nm
Electron charge  e= 1.60E-19 C
electron volt  eV= 1.60E-19 joule
electron mass  mel 9.11E-31 kg
mel 5.11E-01 MeV/c^2
proton mass  mp 1.67E-27 kg
mpev 9.38E+02 MeV/c^2
neutron mass  mn 1.67E-27 kg
mnev 9.40E+02 MeV/c^2
Stefan's constant=  sigma= 5.67E-08 watt/m^2K^4

1. Energies associated with wavelength 0.1 nm
a. Photon
E=hf= hc/wavelength =1240 eV nm/.1 nm =    12400 eV
This photon is in the soft x-ray region.
b. Electron
p=h/wavelength , pc=hc/wavelength, pc=1240 eV nm/.1nm=    12400 eV
energy = p^2/2m for this non-relativistic case
Energy = (pc)^2/2m0c^2 = 12400^2/(2*511000 eV) =    150.450098 eV
c. neutron pc=12400 eV
Energy=12400^2/(2*940MeV)=    0.08178723 eV

2. Energy of confinement within 0.1 nm and 1 fermi
a. Uncertainty in momentum delta p = hbar/2 delta x
delta p c = hbar c/ 2 delta x = 197 eV nm/(2* .1nm)=    985 eV
b. associated energy if delta p = p
This one is non-relativistic, so KE=p^2/2m=(pc)^2/(2 m0c^2)=985^2/2*511000 =
= 0.94933953 eV
c. confine the electron to 1 fermi
now delta p c = 197 MeV fm/2 fm =    98.5 MeV
Being definitely relativistic, this requires
KE=sqrt((pc)^2+(m0c^2)^2) - m0c^2=   97.9903255 MeV
This one is so relativistic that the mass energy can nearly be neglected, giving 98.5 MeV

3. DeBroglie wavelengths for high speed particles
a. 4 MeV electron
wavelength = hc/pc = hc/sqrt((KE+m0c^2)^2-(m0c^2)^2)
wavelength = 1240 MeV fm/sqrt((4 +.511)^2-.511^2) =    276.664436 fm
non-relativistic would give wavelength = 1240/sqrt(2*.511*4) =     613.290506 fm
b. 1 MeV neutron
wavelength=1240 MeV fm/sqrt((1 +940)^2-940^2)=    28.5974635 fm
non-relativistic would give wavelength =   1240/sqrt(2*940*1) =  28.6248205 fm
c. 20keV electron
wavelength=1240 eV nm/sqrt(20000+511000)^2-511000^2) =     8589.59778 fm
In this case the non-relativistic approach would give
wavelength = h/sqrt(2m0E)=hc/sqrt(2 m0c^2E)=
=1240 MeV fm/sqrt(2*.511*.02) =   8673.23751 fm