Formulas to Remember
Additional Formulae and Equations in Modern Physics:
ELECTRONIC TRANSITIONS IN HYDROGEN-LIKE ATOMS
- Rydberg formula:
- Where:
- (R_H) is the Rydberg constant (=1.09737\times10^7 \text{ m}^{-1})
- (n_i) is the initial quantum number of the electron
- (n_f) is the final quantum quantum number of the electron.
X-RAY SPECTRA
-
Moseley’s law:
-
Where:
-
(\nu) is the frequency of the emitted X-ray
-
(k) is a constant
-
(Z) is the atomic number of the target element
-
(b) is a constant that depends on the experimental arrangement.
-
Characteristic X-rays:
-
K-alpha line: Transition from (n=2) to (n=1)
-
K-beta line: Transition from (n=3) to (n=1)
-
L-alpha line: Transition from (n=3) to (n=2)
-
L-beta line: Transition from (n=4) to (n=2)
PARTICLE PHYSICS
-
Mass-energy equivalence (Einstein’s equation):
-
Where:
-
(E) is the energy
-
(m) is the mass
-
(c) is the speed of light
-
Pair production and annihilation:
-
Where:
-
(\gamma) is a high-energy photon
-
(e^+) is a positron
-
(e^-) is an electron
SEMICONDUCTOR PHYSICS
- Ohm’s Law for Semiconductors:
-
Drift velocity:
-
Where:
-
(V_d) is the drift velocity;
-
(\mu) is the mobility of charge carriers
-
(E) is the electric field strength.
-
Diffusion Equation:
-
Where:
-
(D) is the diffusion coefficient of the carriers;
-
(k_B) is the Boltzmann constant;
-
(e) is the elementary charge;
-
(T) is the temperature.
-
Einstein Relation:
-
Where:
-
(k) is the Boltzmann constant;
-
(T) is the temperature;
-
(\mu) is the mobility of the carriers;
-
(q) is the charge of the carrier.
-
P-N Junction:
- Where:
- (I) is the current through the junction;
- (I_S) is the reverse saturation current;
- (V) is the voltage applied to the junction;
- (T) is the temperature;
- (k_B) is the Boltzmann constant.
