# 20.5 Energy of Nuclear Reactions and Nuclear Binding Energy

PRE-HEALTH PREP

Nuclear reactions release a LARGE amount of energy as mass is converted to energy.

E = Δmc2

Δm, the mass defect, must be in kg (1amu = 1.67 × 10-27kg)
c = 3.0 × 108m/s (speed of light)

Mass Defect (Δm) – The difference in mass between the products and reactants of a nuclear reaction
(the products will always weigh less—the mass lost is converted to energy)

Calculate the amount of energy released for the nuclear fission of one uranium-235 atom.

Isotope/ Particle Mass
235.04393amu
1.00866amu
141.91643amu
90.92345amu

## Nuclear Binding Energy (total vs. per nucleon)

-The energy that holds the nucleus together
-56Fe has the highest nuclear binding energy per nucleon and typically the closer in mass you are to 56, the higher the nuclear binding energy per nucleon.

E = Δmc2

Δm, the mass defect, must be in kg (1amu = 1.67 × 10-27kg)
c = 3.0 × 108m/s (speed of light)

Mass Defect (Δm) – The difference between the nuclear mass and the mass of the constituent nucleons
A nucleus always weighs less than its constituent nucleons

CALCULATING NUCLEAR BINDING ENERGY (per nucleon)
1. Calculate the mass defect (Δm = actual mass – predicted mass)
2. Convert to kg (6.02 × 1023 amu = 1g or 1amu = 1.66 × 10-27 kg)
3. Plug into E = Δmc2
4. Divide by mass number (mass # = number of nucleons)

Calculate the nucelar binding energy per nucleon for iron-56 and uranium-235

Nuclide/ Particle Mass
1.00728amu
1.00866amu
235.04393amu
55.93494amu