Equations/Constants to know

Number density equation

N = (rho * N_A) / M or N = (m N_A) / (V * M)

rest mass equation

E_0 = m_0 * c^2

conversion from amu to MeV

1 amu = 931.5 MeV

rest mass energy of an electron

0.511 MeV (511 keV)

Relativistic mass correction factor

gamma = 1 / sqrt(1 - v^2/c^2)

Wavelength of particles equation

lambda = h / p (de Broglie wavelength)

Momentum of nonzero rest mass particle equation

p = gamma*m_0 *v

Derive momentum in terms of kinetic energy for a
particle

Relativistic: p = sqrt(KE^2 + 2*KE*m_0*c^2) / c | Non-relativistic: p = sqrt(2*m * KE)

Planck’s constant in 𝑒𝑉 ∗ 𝑠

h = 4.1357 x 10^-15 eVs

Speed of light

c = 3.00 x 10^8 m/s

Relativistic momentum and wavelength

p = (h / lambda) = gamma*m_0 *v => lambda = h / (gamma *m_0 * v)

Zero rest-mass particle energy and momentum

E = p * c (or p = E / c)

Boltzmann's constant in 𝑒𝑉/k

k_B = 8.617 x 10^-5 eV/K

Convert half-life to decay constant and vice versa

lambda = ln(2) / t_(1/2) or t_(1/2) = ln(2) / lambda

Decay constant to mean-life

tau = 1 / lambda

Convert between Ci and Bq

1 Ci = 3.7 x 10^10 Bq (1 Bq = 1 decay/sec)

Q-value equation

Q = (m_reactants - m_products) c^2 or Q = (M_initial - M_final) 931.5 MeV

Mass defect equation

Delta m = [Z m_p + (A - Z) m_n] - m_nucleus

Number of Neutrons*Mass of a neutron (1.008665)

Number of Protons*Mass of a proton (1.007825)

This is the Volume term. This term represents the attractive forces initially exhibited by the nucleons, and has A in the answer because the numbers of bonds between each nucleon are fixed and proportional to the mass number (A).

This is the Surface Term. This term corrects for the volume term, because the outer (surface) nucleons have less bonds than the inner ones. Because we are accounting for the outer nucleons, it is proportional to A^⅔ which is the surface area.

This is the Coulomb term. This term corrects for the repulsion forces between protons in the nucleus. It accounts for the number of proton pairs as well as the radius of the atom

This is the Asymmetry term. This term corrects for the imbalance between the number of protons and neutrons (hence “asymmetry”)

This is the Pairing term. This term reflects how nucleons tend to form spin-zero pairs.