Physical constants
Boltzmann's constant k= 1.38066E-23 J/K
k= 0.00008617 eV/K
Atomic mass unit u= 1.66E-27 kg
umev= 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
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
mpg 0.93827231 GeV/c^2
neutron mass mn 1.67E-27 kg
mnev 9.40E+02 MeV/c^2
mng 0.93956563 GeV/c^2
Stefan's constant= sigma= 5.67E-08 watt/m^2K^4
Nuclear distance unit fermi 1.00E-15 m (a femtometer)
cross section unit barn= 1.00E-28 m^2
barn= 100 fm^2
common combo for scattering ke^2 1.44 MeV fm
First Bohr orbit radius a0 a0 0.0529 nm
Bohr magnetion mub 5.79E-05 eV/T
muba 9.27E-24 A m^2 A=ampere
#3 Energy of incident photons and neutrons to give N a recoil
energy of 1.4 MeV
a. Photon energy required comes from Compton scattering formula for
scattering at 180°
At 180 degrees the wavelength change is given by 2hc/mc^2 where m is
nitrogen mass
For the photon of wavelength w and energy E, delta w/w =delta E/E.
This shakes down to a photon energy E=sqrt(delta E mc^2/2)
The mass of the N-14 nucleus is 14.003*931.5 MeV/c^2 =
13043.7945 MeV/c^2
The photon energy required is then = sqrt(1.4 MeV*1.304E4 MeV/2) =
95.55446693 MeV/c^2
This is much more energy than you can get from a nuclear reaction,
so the particle is not a photon.
b. Neutron energy required comes from elastic collision.
For m1<<m2 and headon, the change in momentum for m1 is twice
its original momentum
(I.e., it bounces straight back with essentially its original speed.)
.5*mN*vN^2 = 1.4 MeV = E, but mN*vN=2m(neutron)*v(neutron),
so KE neutron = Em(nitrogen)/(4*m(neutron)) = (1.4 MeV)(1.304E4 MeV)/(4*940MeV)
KE neutron = 4.855319149 MeV
#6 Mass of U-235 nucleus and atom
92 protons at 938.2723 MeV = 86321.05252 MeV/c^2
143 protons at 939.5656 MeV= 134357.88509 MeV/c^2
minus binding energy 235*7.59= 1783.65000 MeV/c^2
Net mass of nucleus = 218895.28761 MeV/c^2
Add electrons
=92*.511 MeV = 47.01200 MeV/c^2
Mass of atom = 218942.29961 MeV/c^2
#7 Binding energies for manganese, iron and cobalt
For Mn-55, E/A=482.1/55= 8.765454545 MeV
For Fe-54, E/A=471.8/54= 8.737037037 MeV
For Fe-56, E/A=492.3/56= 8.791071429 MeV
For Fe-57, E/A=499.9/57= 8.770175439 MeV
For Fe-58, E/A=510.0/58= 8.793103448 MeV
For C0-59, E/A=517.3/59= 8.76779661 MeV
#11. The binding energy for Fe-55 is 481 MeV.
The Weizsaecker formula gives
E(odd-even)=15.75*55-17.8*55^(2/3)-.711*26^2/55^(1/3)-23.7*9/55 =
= 478.5552927 MeV
For Co-57 the binding energy is 498 MeV
E(odd-odd)=15.75*57-17.8*57^(2/3)-.711*27^2/57^(1/3)-23.7*9/57-11.18/sqrt(57)
=
= 494.2112174 MeV
For Ni-58 the binding energy is 506 MeV. The Weizsaecker formula gives
E(even-even)=15.75*58-17.8*58^(2/3)-.711*28^2/58^(1/3)-23.7*4/58+11.18/sqrt(58)
=
= 502.6193239 MeV
#15 A factor of 32 is 5 halflives, halflife=1 s
#18 Age = half-life*ln(R0/R)/ln(2)=5730y*ln(25/16.7)/ln(2)= 3335.318355 years
#20 Neutron binding energies.
a. Last neutron in O-17: Energy = 131.77-127.62= 4.15 MeV
b. Last neutron in O-18:Energy =139.81-131.77= 8.04 MeV
#21Fe-55 + electron=Mn-55+neutrino
b. The xray is likely a K-alpha xray for Mn, so approximately 13.6*(25-1)^2*3/4 assuming shielding by the remaining 1s electron. This gives 5875 eV.
#22 Identify the unknown
a. X has Z=13 and A=23 which is Al-23
b. X has Z=78 and A=190 which is Pt-190
c. X has Z=5 and A=11 which is B-11
d. Z has decreased, so positron
e. X has Z=1 and A=1 which is a proton
#23 Energy release = mass of alpha + U235-Pu239 =
=28.296+1783.897-1806.948 = 5.245 MeV
KE of alpha=Q(A-4)/A=5.25*235/239= 5.162133891 MeV
#29 Source speeds for given energy change
a. v= c*delta E/E =3E8m/s*1E-5/129000 = 0.023255814 m/s
b. v= c*delta E/E =3E8m/s*1E-8/14400 = 0.000208333 m/s
#40 Since one gram corresponds to 1 Curie, then 0.1 microcurie
1e-10kg*6E23/(226*1E-3)= 2.65487E+14 atoms