Mass Defect & Binding Energy – AP Physics 2

Mass-Energy Equivalent

$$ E = \Delta m c^2 $$

Definitions

Mass Defect ($\Delta m$): Missing mass holding the nucleus together ($Z M_H + N M_n - M_{atom}$).

Binding Energy ($BE$): Energy required to completely disassemble a nucleus.

$BE/A$: Binding energy per nucleon. Higher = more stable nucleus (peaks around Fe-56).

Constants (AP Exam)

$1 \text{ u} = 931.5 \text{ MeV/c}^2$

$M_H$ (atom): 1.007825 u

$M_n$ (neutron): 1.008665 u

Tags

nuclearmass defectbinding energystability

Isotope Analysis

Target Isotope:	He-4
Protons ($Z$) / Neutrons ($N$):	2 / 2

Individual Parts Mass (Expected):
Bound Isotope Mass (Actual):
Mass Defect ($\Delta m$):

Binding Energy ($BE$):
BE per Nucleon ($BE/A$):

Target Isotope

Notice how the bound nucleus weighs less than the sum of its unbound protons and neutrons. That lost mass converted geometrically into the strong force binding energy.