What is tension force?

Tension force is a pulling force transmitted along a string, rope, wire, or cable when forces act from opposite ends. It acts parallel to the connector and pulls away from attached objects.

What is the primary formula for tension?

For a stationary hanging mass, the formula is T = mg. For an accelerating mass, the general formula is T = m(g ± a).

Is tension constant throughout a rope?

In an ideal massless and frictionless rope, tension magnitude is uniform throughout its entire length. In real heavy ropes, tension increases higher up the rope to support the rope's own weight.

How does acceleration affect elevator cable tension?

Upward acceleration increases cable tension (T = m(g + a)), making objects feel heavier. Downward acceleration decreases cable tension (T = m(g - a)).

What is an Atwood machine?

An Atwood machine is a classic physics setup featuring two masses connected by a string over a pulley. It demonstrates Newton's second law under constant acceleration.

How does tension relate to Newton's Third Law?

Ropes transmit equal and opposite reaction forces at both ends. The string pulls on the object, and the object pulls back on the string with equal magnitude in the opposite direction.

What is the De Broglie Wavelength?

The De Broglie Wavelength is the wavelength associated with a moving particle, defined by λ = h/p. It proves that all matter exhibits wave-particle duality.

What factors influence the De Broglie Wavelength?

Wavelength depends inversely on particle mass (m) and velocity (v). Increasing either mass or speed reduces the wavelength.

Why don't macroscopic objects show wave behavior?

Because macroscopic bodies have large masses, their De Broglie wavelengths are extremely tiny (10^-35 m), far smaller than atomic dimensions, preventing observable wave interference.

How does De Broglie Wavelength relate to Kinetic Energy?

Wavelength is inversely proportional to the square root of kinetic energy: λ = h / sqrt(2mK).

Can massive particles like C60 molecules show wave behavior?

Yes! Experiments have successfully demonstrated quantum wave interference using large Buckminsterfullerene (C60) molecules, proving that wave properties apply to complex structures if isolated from environmental decoherence.

What experiment definitively proved the wave nature of electrons?

The Davisson-Germer Experiment (1927) definitively proved electron wave properties by demonstrating that electrons scatter off nickel crystals in a diffraction pattern matching Bragg’s Law.

How does De Broglie wavelength explain Bohr's stationary orbits?

De Broglie proposed that electrons form standing waves around an atomic nucleus. A stable orbit requires an integer number of whole wavelengths to fit the orbit's circumference (2πr = nλ), directly deriving Bohr's quantization condition.

What is the best branch of physics to start with as a beginner?

Classical Mechanics is the best starting point because it deals with tangible everyday phenomena like gravity, speed, and forces, making concepts easy to visualize.

Do I need calculus to learn physics from scratch?

No. Algebra-based physics covers all core principles using basic algebra, geometry, and trigonometry. Calculus is only needed for advanced university-level courses.

What is the fastest way to understand physics formulas?

Focus on the physical relationships between variables rather than memorizing formula symbols.

Can I self-learn physics without a formal teacher?

Yes, using structured roadmaps, online simulations (like PhET), textbooks, and active practice problems allows you to self-learn physics effectively.

What is the difference between heat and temperature?

Temperature measures average kinetic energy of particles, whereas heat is the total thermal energy transferred between objects.

Why does metal feel colder than wood at room temperature?

Metals have higher thermal conductivity, drawing heat away from skin faster than wood even when at identical temperatures.

How is specific heat capacity measured in a lab?

It is measured via electrical calorimetry using the formula c = Pt / (m ΔT) with an immersion heater and insulated vessel.

Can SUVAT equations be used when acceleration is not constant?

No, SUVAT equations strictly apply only when acceleration is uniform and constant. For variable acceleration, calculus techniques must be used.

What is the difference between displacement and distance in SUVAT?

Displacement (s) is a vector measuring overall change in position from start to end point, while distance is a scalar measuring total path length traveled.

Why is acceleration negative when an object slows down?

Deceleration means final velocity is less than initial velocity (v < u), resulting in a negative rate of change for velocity relative to the positive direction of motion.

What value of g should I use for free fall SUVAT problems?

Standard gravity is approximately 9.81 m/s², though many physics courses round to 9.8 m/s² or 10 m/s² for easier calculation.

How do SUVAT equations apply to 2D projectile motion?

SUVAT equations apply independently to the vertical axis with acceleration a = -g, while the horizontal axis experiences zero acceleration (a = 0).

Why can't objects with mass travel at the speed of light?

As velocity approaches c, the Lorentz factor approaches infinity, requiring an infinite amount of energy to accelerate any massive object to light speed.

What is the twin paradox in special relativity?

The twin paradox compares a traveling twin and an Earth-bound twin. The space traveler returns younger due to time dilation caused by relativistic speeds and frame-changing acceleration.

Does length contraction affect dimensions perpendicular to motion?

No, length contraction occurs exclusively along the direction of relative travel. Perpendicular axes retain their original proper dimensions.

How does special relativity differ from general relativity?

Special relativity addresses flat spacetime and non-accelerating inertial frames, while general relativity incorporates gravitational acceleration and curved spacetime.

What is the difference between centripetal force and centrifugal force?

Centripetal force is a real net inward force causing circular path trajectory. Centrifugal force is a fictitious outward effect felt in rotating non-inertial reference frames due to inertia.

Why does a vehicle slide outward on an icy curve?

Static friction provides required centripetal force on flat turns. Ice lowers available friction below required mv^2/r, causing inertia to move the vehicle tangentially outward.

Is work done by a centripetal force in uniform circular motion?

No work is done because centripetal force acts strictly perpendicular (90 degrees) to displacement at all points along the circular path.

How does changing velocity affect centripetal acceleration?

Centripetal acceleration varies quadratically with speed (v^2/r). Doubling velocity quadruples inward acceleration requirements.

Is mechanical energy conserved during all collisions?

Total energy is conserved in every collision. However, kinetic energy is only conserved in perfectly elastic collisions. In inelastic collisions, kinetic energy converts into heat, deformation, and sound.

Can potential energy have a negative value?

Yes, potential energy can be negative if the object lies below your chosen zero reference level. Only relative changes in potential energy matter in calculations.

What is the relationship between net work and energy?

Work is the mechanism of energy transfer. The net work done on an object equals its change in kinetic energy according to the Work-Energy Theorem.

Home > Physics Notes > Modern Physics

Modern Physics — Quantum Mechanics, Relativity & Nuclear Physics

Modern Physics explores quantum mechanics, special relativity ( $E=mc^2$ ), wave-particle duality, photoelectric effect equations, de Broglie wavelength formulas, and nuclear half-life calculations with clear study notes and practice MCQs.

Modern Physics Study Notes

Before diving into quantum mechanics and relativity concepts, read our beginner guide on how to learn physics easily to build strong conceptual fundamentals.

1. Special Relativity (Einstein, 1905)

Special relativity rests on two postulates: (1) The laws of physics are identical in all inertial reference frames. (2) The speed of light in a vacuum (c = 3×10&sup8; m/s) is constant for all observers, regardless of the motion of the source or observer.

Consequences: time dilation (moving clocks run slow), length contraction (moving objects appear shorter in the direction of motion), and mass-energy equivalence: E = mc².

2. The Photoelectric Effect and Quantum Theory

Understand photons, Planck’s constant ( $E=hf$ ), and the equation for photoelectric effect with work function calculations: equation for photoelectric effect.

3. Wave-Particle Duality and de Broglie

Master wave-particle duality, matter waves, and the de Broglie wavelength formula ( $\lambda = h/mv$ ): wave-particle duality, de broglie wavelength formula.

4. Nuclear Physics

Learn nuclear binding energy, alpha beta gamma decay equations, and how to find half life using exponential decay formulas: alpha beta gamma decay, how to find half life) photon emitted. All governed by E = mc².

Modern Physics Formula Sheet & Quantum Equations

Essential de Broglie equations, photoelectric formulas, mass-energy equivalence, and radioactive half-life formulas for exam revision. de Broglie equations, half-life formulas)

Mass-Energy

E = mc²

Energy = mass × speed of light squared

Unit: J (Joules)

Photon Energy

E = hf

Energy = Planck constant × frequency

Unit: J (Joules)

de Broglie

λ = h/mv

Wavelength = Planck constant / momentum

Unit: m (metres)

Time Dilation

t = t&sub0;/√(1−v²/c²)

Time experienced by moving observer

Unit: s (seconds)

Photoelectric

KE⊂max; = hf − φ

Max KE of emitted electron (φ = work function)

Unit: J (Joules)

Radioactive Decay

N = N&sub0;e&sup-λt

Number of undecayed nuclei at time t

Unit: count

Frequently Asked Questions About Modern Physics

Clear answers to key questions about wave-particle duality, photoelectric effect, and nuclear fission versus fusion

What is special relativity?

Special relativity is Einstein’s theory based on two postulates: physical laws are identical in all inertial frames, and the speed of light in a vacuum ( $c = 3\times 10^8\text{ m/s}$ ) is constant for all observers. It leads to time dilation and mass-energy equivalence ( $E=mc^2$ ).

What is the photoelectric effect?

The photoelectric effect is the emission of electrons from a material surface when light of sufficient frequency shines on it, proving the photon (particle) nature of light ( $KE_{max} = hf - \phi$ ).

What is wave-particle duality?

Wave-particle duality is the concept that matter and light exhibit both wave-like and particle-like properties, described by the de Broglie wavelength formula ( $\lambda = h/p$ ).

What is nuclear fission vs fusion?

Nuclear fission is the splitting of a heavy atomic nucleus into smaller fragments, releasing energy. Nuclear fusion is the combining of light atomic nuclei to form a heavier nucleus under extreme heat and pressure.

For interactive quantum models and photoelectric effect visual simulations, explore resources at PhET Interactive Simulations.

Modern Physics — Quantum Mechanics, Relativity & Nuclear Physics

Modern Physics Study Notes

1. Special Relativity (Einstein, 1905)

2. The Photoelectric Effect and Quantum Theory

3. Wave-Particle Duality and de Broglie

4. Nuclear Physics

Modern Physics Formula Sheet & Quantum Equations

Mass-Energy

E = mc²

Photon Energy

E = hf

de Broglie

λ = h/mv

Time Dilation

t = t&sub0;/√(1−v²/c²)

Photoelectric

KE⊂max; = hf − φ

Radioactive Decay

N = N&sub0;e&sup-λt

Frequently Asked Questions About Modern Physics

Related Physics Topics

Electricity & Magnetism

Wave Physics

Physics Formulas List