Comprehensive notes for Chapter 21 Nuclear Physics. Covers Atomic Nucleus, Isotopes, Mass Spectrograph, Mass Defect, Binding Energy, and Radioactivity.
Structure: Central positive core containing protons and neutrons (nucleons). Radius $$ \approx 10^{-15} m $$ (10,000 times smaller than atom).
Charge Number (Z): Number of protons.
Mass Number (A): Total protons + neutrons. $$ A = Z + N $$.
Isotopes: Atoms with same Z but different A (e.g., $$ ^1H, ^2H, ^3H $$).
Device to separate isotopes and measure their masses.
Principle: Ions are accelerated by potential V and then deflected by magnetic field B. $$ \frac{mv^2}{r} = qvB \implies r = \frac{mv}{qB} $$.
Mass Formula: $$ m = \frac{q B^2 r^2}{2V} $$. Mass is proportional to $$ r^2 $$.
Mass Defect ($$ \Delta m $$): Difference between sum of nucleon masses and nucleus mass. $$ \Delta m = Zm_p + (A-Z)m_n - M_{nuc} $$.
Binding Energy (B.E): Energy equivalent to mass defect. $$ B.E = \Delta m c^2 $$.
B.E per Nucleon: Maximum for Iron ($$ 8.8 MeV $$). Fission/Fusion release energy to move towards this stability.
Definition: Spontaneous emission of radiation by unstable nuclei ($$ Z > 82 $$).
Types:
Definition: Time required for half of the radioactive atoms to decay.
Formula: $$ N = N_0 (\frac{1}{2})^n $$ where $$ n = \frac{t}{T_{1/2}} $$ is number of half lives.
Decay Law: Rate of decay is proportional to number of atoms present. $$ \frac{\Delta N}{\Delta t} = -\lambda N $$.