This chapter explores the atomic structure, detailing the models of atoms proposed by J.J. Thomson and Ernest Rutherford. Understanding these concepts is crucial for grasping the foundation of modern physics.
ATOMS – Formula & Equation Sheet
Essential formulas and equations from Physics Part - II, tailored for Class 12 in Physics.
This one-pager compiles key formulas and equations from the ATOMS chapter of Physics Part - II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
E = mc²
E represents energy (in joules), m is mass (in kg), and c is the speed of light (≈ 3 × 10⁸ m/s). This formula demonstrates mass-energy equivalence and is fundamental in relativity.
F = k * (q₁ * q₂) / r²
F is the electrostatic force between two charges (N), k is Coulomb's constant (≈ 8.99 × 10⁹ N m²/C²), q₁ and q₂ are the charges (C), and r is the distance between them (m). This illustrates the inverse square law of electrostatics.
r = n² * (h² / (4π² * k * m * e²))
r is the radius of the n-th orbit (m), n is the principal quantum number, h is Planck’s constant, k is Coulomb's constant, m is the mass of the electron, and e is the elementary charge. This relates to the radius of electron orbits in the Bohr model.
L = n * (h / 2π)
L is the angular momentum of the electron (kg m²/s), n is the principal quantum number, and h is Planck's constant. This quantization condition shows allowed electron orbits around the nucleus.
E_n = - (k * e²) / (2 * r)
E_n is the total energy of the n-th orbit (J), k is Coulomb's constant, e is the charge of the electron, and r is the radius of the orbit. This formula describes the bound state energy of the electron.
n = v * r / (2π)
n is the frequency of the revolving electron, v is its speed, and r is the radius of the orbit. It connects frequency with circular motion in atomic orbits.
ΔE = hν
ΔE is the change in energy (J), h is Planck's constant, and ν is the frequency of emitted or absorbed radiation (Hz). This fundamental concept relates energy transitions to light emission/absorption.
λ = c / ν
λ is the wavelength (m), c is the speed of light (≈ 3 × 10⁸ m/s), and ν is the frequency. This formula connects the speed of light with its wave properties.
d = (2Ze² / (h^2)) * (1/K)
d is the distance of closest approach (m), Z is the atomic number, and K is the kinetic energy of the incoming α-particle (J). This relates to the scattering process in Nuclear Physics.
E = hc / λ
E is the energy of a photon (J), h is Planck's constant, and λ is the wavelength (m). This expression is used to compute photon energies from their wavelengths.
Equations
V = IR
V is voltage (V), I is current (A), and R is resistance (Ω). This equation represents Ohm's Law, relating voltage, current, and resistance.
F = ma
F is force (N), m is mass (kg), and a is acceleration (m/s²). This fundamental principle in Newton's Second Law relates mass and acceleration to force.
p = mv
p is momentum (kg m/s), m is mass (kg), and v is velocity (m/s). This equation defines momentum in classical mechanics.
E_k = 1/2 mv²
E_k is kinetic energy (J), m is mass (kg), and v is velocity (m/s). This equation describes the energy of an object in motion.
P = W/t
P is power (W), W is work done (J), and t is time (s). This formula calculates the rate of work done or energy conversion.
ρ = m/V
ρ is density (kg/m³), m is mass (kg), and V is volume (m³). This relationship defines how mass is distributed in space.
a = Δv/Δt
a is acceleration (m/s²), Δv is change in velocity (m/s), and Δt is change in time (s). This formula expresses how velocity changes over time.
v = u + at
v is final velocity (m/s), u is initial velocity (m/s), a is acceleration (m/s²), and t is time (s). This motion equation describes velocity changes over time.
s = ut + 1/2 at²
s is displacement (m), u is initial velocity (m/s), a is acceleration (m/s²), and t is time (s). This equation relates displacement to time under uniform acceleration.
E_p = mgh
E_p is potential energy (J), m is mass (kg), g is acceleration due to gravity (≈ 9.81 m/s²), and h is height (m). This formula calculates gravitational potential energy.
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