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JEE Advanced Physics and Chemistry Key Concepts

Essential formulas, thermodynamic relations, electromagnetism laws, and organic reaction rules for JEE Advanced preparation.

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Carnot Engine Efficiency

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Carnot Engine Efficiency

Efficiency is

η = 1 - \frac{T _{C}}{T _{H}}

, where temperatures must be in Kelvin.

Magnetic Field on Axis of Circular Current Loop

B = \frac{μ _{0} i R ^{2}}{2 ( R ^{2} + x ^{2} ) ^{3/2}}

, along the axis of symmetry.

Maxwell Displacement Current

i_{d} = ε_{0} \frac{d Φ _{E}}{d t}

, arising from time-varying electric flux.

De Broglie Wavelength of Accelerated Electron

λ = \frac{h}{2 m _{e} q V} \approx \frac{1.227}{V} nm

for potential

V

Einstein Photoelectric Equation

K_{m a x} = h ν - Φ_{0} = e V_{0}

, where

Φ_{0}

is the work function and

V_{0}

is stopping potential.

Young's Double-Slit Fringe Width

β = \frac{λ D}{d}

, where

D

is screen distance and

d

is slit separation.

LC Circuit Natural Angular Frequency

ω_{0} = \frac{1}{L C}

rad/s for an ideal LC resonant loop.

Escape Velocity from Spherical Body

v_{e} = \frac{2 GM}{R} = 2 g R

, independent of the escaping mass.

Moment of Inertia of Solid Cylinder about Axis

I = \frac{1}{2} M R^{2}

, identical to a uniform solid disk.

Doppler Shift for Sound (Approaching Source)

f^{'} = f (\frac{v}{v - v _{s}})

, observing higher pitch.

Poynting Vector in EM Wave

S = \frac{1}{μ _{0}} (E \times B)

, representing directional power flux density.

Quality Factor of Series LCR Resonator

Q = \frac{1}{R} \frac{L}{C} = \frac{ω _{0} L}{R}

, measuring sharpness of resonance.

Adiabatic Reversible Gas Process

P V^{γ} = constant

, and

T V^{γ - 1} = constant

, with

γ = C_{p} / C_{v}

Arrhenius Equation for Rate Constant

k = A e^{- E_{a} / (R T)}

, relating activation energy

E_{a}

to temperature.

Nernst Equation at 298 K

E = E^{\circ} - \frac{0.0591}{n} lo g_{10} Q

, adjusting half-cell potential.

Crystal Field Splitting in Octahedral Complex

d

-orbitals split into lower

t_{2 g}

(

d_{x y}, d_{y z}, d_{x z}

) and higher

e_{g}

(

d_{z^{2}}, d_{x^{2} - y^{2}}

Hückel Rule for Aromaticity

A planar, completely conjugated cyclic system requires

(4 n + 2)

delocalized

π

electrons.

Markovnikov Rule for Alkene Addition

Electrophile

H^{+}

bonds to the carbon with more hydrogens, creating the more stable carbocation.

Raoult's Law for Ideal Binary Solutions

P_{total} = P_{A}^{\circ} x_{A} + P_{B}^{\circ} x_{B}

, where

x

denotes liquid mole fraction.

Elevation in Boiling Point

Δ T_{b} = i K_{b} m

, where

i

is van 't Hoff factor and

m

is molality.

First-Order Reaction Half-Life

t_{1/2} = \frac{l n 2}{k} \approx \frac{0.693}{k}

, independent of initial concentration.

Standard Gibbs Free Energy and Equilibrium

Δ G^{\circ} = - R T ln K = - 2.303 R T lo g_{10} K

Henderson-Hasselbalch Equation for Acidic Buffer

pH = p K_{a} + lo g_{10} (\frac{[ Conjugate Base ]}{[ Acid ]})

Faraday's First Law of Electrolysis

m = Z I t = \frac{E}{96500} I t

, relating mass deposited to passed charge.

Clausius-Clapeyron Vapor Pressure Relation

ln (\frac{P _{2}}{P _{1}}) = - \frac{Δ H _{vap}}{R} (\frac{1}{T _{2}} - \frac{1}{T _{1}})

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