Energy Changes in Nuclear ReactionsEnergy and mass aretwo sides of the same coin.

E = mc2c = 3.00 x 108 m/s

m = mass, in kgE = energy, in J

When a system loses/gains energy, it loses/gains mass. In chemical reactions, this mass change is nearlyundetectable, so we speak of mass as being“conserved,” when it really isn’t. The amount of“mass-and-energy-together,” however, IS conserved.Mass changes in nuclear reactions are much largerthan in chemical reactions, and are easily measured.All spontaneous nuclear reactions are exothermic.

Nuclear Binding Energy

mass ofnucleus

mass ofnucleons<

(when they AREN’T in anucleus, i.e., if they wereseparated and massed

individually)

“Separate: heavier.Tighter: lighter.”

rest masses: n0 = 1.00866 amu = 1.67493 x 10–24 g p+ = 1.00728 amu = 1.67262 x 10–24 g

e– = 0.0005486 amu = 9.113 x 10–28 g

mass defect = mass of

constituentnucleons

mass ofnucleus–

This “missing” mass is convertedinto energy, which is used tohold the nucleus together.

(or “mass deficiency”)

Use mass defect, E = mc2, and # of nucleons tocalculate binding energy per nucleon (BE/n).

-- large BE/n means great nuclear stability

-- BE/n is largest for Fe-56, meaning:(1) larger-than-Fe-56-nuclei…

(2) smaller-than-Fe-56-nuclei… can undergo fusion

+ ENERGY

+ ENERGY

Both fission and fusion are exothermic.

decay OR can undergo fission

Calculate the binding energy per nucleon of N-14,which has a nuclear mass of 13.999234 amu.

7 p+ (1.00728 amu) = 7.05096 amu7 n0 (1.00866 amu) = 7.06062 amu

14.11158 amu

m.d. = 14.11158 – 13.999234 = 0.11235 amu

0.11235 amu

= 1.8656 x 10–28 kg

= 1.1993 x 10–12 J/nucleon

As a comparison, the BE/n for Fe-56 is 1.41 x 10–12 J/n,which is 8.79 MeV (1 eV = 1.60 x 10–19 J).

amu 10 x 6.02g 1

23

g 1000kg 1

nBE

nmc2

14

)10 x (3 10 x 1.8656 2828

Nuclear Fission Fission requires… slow-moving neutrons.

distance too big;strong force weakens;+/+ repulsion takes over

fast n0slow n0 released n0;free to splitmore nuclei

Important fissionable nuclei: U-233, U-235, Pu-239

chain reaction: one nuclear reaction leads to one or more others

critical mass: the mass of fissionable material requiredto maintain a chain reaction at a constant rate

safe safe criticalmass

(“Run, Forrest, run!”)

supercriticalmass

supercritical mass: the mass above which the chainreaction accelerates

(reactionmaintainedat constant

rate)

Little Boy, later dropped on Hiroshima(“Ah jes’ felt lahk runnING.”)