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Formula Sheets / Physics

Chapter 30

Nuclear Physics

Revise with flashcards Download this chapter (PDF) All Physics formulas (PDF)

Nuclear structure and binding energy Radioactivity and decay laws Fission and fusion

Nuclear structure and binding energy

Radius
$Δ m = Z m_{p} + (A - Z) m_{n} - M,$ $R_{0} \approx 1.2$ fm $;$ density is the same for all nuclei
Mass defect
$Δ m = Z m_{p} + (A - Z) m_{n} - M,$ $E_{b} = Δ m c^{2}$
$1$ u $= 931.5$ MeV $/ c^{2}$

Radioactivity and decay laws

$N = N_{0} e^{- λ t},$ $A = λ N$
Half-life and mean life
$T_{1/2} = \frac{ln 2}{λ} = \frac{0.693}{λ},$ $τ = \frac{1}{λ}$
After n half-lives
$N = N_{0} (\frac{1}{2})^{n}$
Decays
$α : A - 4, Z - 2;$ $β^{-} : Z + 1;$ $β^{+} : Z - 1;$ $γ :$ no change

Fission and fusion

Q-value
$Q = (m_{reactants} - m_{products}) c^{2}$
fission splits heavy nuclei; fusion joins light ones; both raise binding energy per nucleon

Atomic Physics Semiconductors