NDA Physics · Formula sheet

Modern Physics formulas

5 formulas, 13 reference tables and 23 common traps for NDA Physics Modern Physics, grouped by subtopic.

Photoelectric Effect: Light as Particles

The photon — light carries energy in discrete packets E = hf

Energy of a photon

E = hf = \dfrac{hc}{\lambda}

$E$ energy of one photon (J)
$h$ Planck's constant, 6.63 x 10⁻³⁴ J·s
$f$ frequency of the light (Hz)
$c$ speed of light, 3 x 10⁸ m/s
$λ$ wavelength of the light (m)

Cutoff wavelength and the energy-voltage link

Cutoff wavelength of X-rays

\lambda_{min} = \dfrac{hc}{eV}

$λ_min$ shortest (cutoff) wavelength produced
$h$ Planck's constant
$c$ speed of light
$e$ electron charge
$V$ accelerating voltage of the tube

Who explained the photoelectric effect — Einstein and the Nobel Prize

Person / idea	Contribution
Albert Einstein	Explained the photoelectric effect using the photon/quantum idea (1905) NDA 2019 — the photoelectric effect was explained by Albert Einstein (not Bohr, Planck, or Rutherford).
Max Planck	Introduced energy quanta $E = hf$ (Planck's constant); the quantum seed Einstein used
Heinrich Hertz	First OBSERVED the photoelectric effect experimentally (but did not explain it)

Distinguish the OBSERVER (Hertz) from the EXPLAINER (Einstein). The exam asks who explained it — that is Einstein.

Common traps

Brightness does NOT change photon energy

Making light brighter sends MORE photons per second, but each photon still carries the same energy

E = hf

. To raise the energy per photon you must raise the frequency (shift toward blue/UV/X-ray), not turn up the intensity.

Energy grows with frequency, falls with wavelength

E = hf = hc/\lambda

. Since

f

and

\lambda

are inversely related, an option saying "longer wavelength = more energy" is always wrong. Long wavelength (red, radio) = low energy.

Threshold is about FREQUENCY, not intensity

A bright low-frequency beam ejects zero electrons; a faint high-frequency beam ejects them at once. The deciding factor is whether each photon clears the threshold frequency — never the brightness.

Einstein's Nobel was for the photoelectric effect, NOT relativity

A classic distractor pairs Einstein's Nobel Prize with relativity. The 1921 Nobel Prize was awarded specifically for his explanation of the photoelectric effect.

Observed vs explained

Hertz observed the effect; Einstein explained it. The exam wording "explained the phenomenon" points to Einstein.

Cutoff wavelength is inversely related to voltage

Double V does NOT double the wavelength — it halves it. The energy goes up, and higher energy means shorter wavelength. Distractors offering "doubled" or "four times" reverse the relationship.

Atomic Structure: Models, Shells, and Energy

Learn this subtopic in the notes

Bohr's model — electrons in stable orbits without radiating

Bohr energy levels of hydrogen

E_n = -\dfrac{13.6}{n^2}\ \text{eV}

$E_n$ energy of the n-th orbit (eV)
$n$ orbit number (1, 2, 3, ...)
$13.6 eV$ magnitude of the ground-state (n=1) energy of hydrogen

Cathode rays — the discovery of the electron

Property of cathode rays	Correct statement
What they are	A stream of electronsQ
Direction of travel	From cathode to anode (negative to positive) NDA 2019 — the FALSE statement was "cathode ray particles start from the anode and move towards the cathode." They go cathode to anode.
Charge	Negative
Path	Straight line; deflected by electric and magnetic fields

The most common trap reverses the direction: cathode rays start at the CATHODE, not the anode.

Rutherford's alpha-scattering — the nucleus

Observation	Conclusion
Most alpha particles pass straight through	Atom is mostly empty space
A few alpha particles deflect at large angles / rebound	A tiny, dense, positively charged nucleus exists NDA 2021 — Rutherford's alpha-scattering experiment discovered the atomic NUCLEUS.
Almost all mass concentrated centrally	Nucleus holds the protons (and neutrons)

Rutherford = nucleus. Do not confuse with Chadwick (neutron) or Thomson (electron).

Electron shells and ionisation energy — the fixed numbers

Quantity	Value	How to get it
K-shell (n=1) capacity	2 electrons	$2n^2 = 2(1)^2 = 2$
L-shell (n=2) capacity	8 electrons	$2n^2 = 2(2)^2 = 8$
M-shell (n=3) capacity	18 electrons	$2n^2 = 2(3)^2 = 18$ NDA 2021 — the M-shell holds a maximum of 18 electrons.
N-shell (n=4) capacity	32 electrons	$2n^2 = 2(4)^2 = 32$
Hydrogen ionisation energy	13.6 eV	Depth of the n=1 ground stateQ
Energy in atomic bonds	Chemical energy	Stored in the links between atomsQ

Shell capacity is 2n². Hydrogen ionisation energy 13.6 eV is the single most-repeated number in the chapter.

Common traps

Cathode to anode, never anode to cathode

The single most-tested cathode-ray trap is the direction. Rays start at the CATHODE (the negative electrode) and move to the anode. Any option saying "from anode to cathode" is the false statement.

Rutherford found the nucleus, not the neutron

Rutherford's scattering experiment discovered the NUCLEUS. The NEUTRON was discovered later by James Chadwick. Distractors swap these two.

Bohr's electrons radiate only when they JUMP

An electron sitting in an allowed orbit does NOT radiate. Radiation (a photon) appears only during a transition between orbits — emitted when dropping down, absorbed when moving up.

Shell capacity is 2n², not a fixed 8

The "octet" of 8 is only the L-shell. The general rule is

2n^2

: M (n=3) holds 18, N (n=4) holds 32. Do not cap every shell at 8.

Hydrogen ionisation energy = 13.6 eV (positive energy IN)

The ground-state energy is

-13.6

eV; the ionisation energy (the energy you must supply to free the electron) is

+13.6

eV. The exam answer is 13.6 eV.

Nuclear Physics: Fission, Fusion, and Reactors

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Nuclear energy — fission, fusion, and E = mc²

Mass-energy equivalence

E = mc^2

$E$ energy released (J)
$m$ mass lost / converted (kg)
$c$ speed of light, 3 x 10⁸ m/s

The nuclear reactor — controlled fission and its parts

Reactor component	Role
Fuel (uranium-235)	Undergoes fission to release energy
Moderator (graphite, heavy water)	Slows down fast neutrons
Control rods (cadmium, boron)	Absorb neutrons to control the reaction rate
Coolant	Removes heat from the core
A mechanism to reduce CO₂ emission	Does NOT belong to a reactor NDA 2024 — the item that does NOT belong to a nuclear reactor is "a mechanism to reduce CO₂ emission" (reactors emit no CO₂ in the first place).

Principle = controlled fission. The odd-one-out trap is the CO₂-reduction mechanism — nuclear power produces no CO₂, so no such part exists.

Nuclear fuel, measuring radioactivity, and radiation types

Radiation	What it is	Stopped by
Alpha (α)	Helium nucleus (2 protons + 2 neutrons), charge +2	A sheet of paper Most ionising, least penetrating.
Beta (β)	Fast electron, charge -1	A few mm of aluminium
Gamma (γ)	High-energy electromagnetic wave, no charge	Thick lead or concrete Least ionising, most penetrating.

Penetration: γ > β > α. Ionising power: α > β > γ. Alpha is stopped by paper; gamma needs thick lead.

Common traps

Fission splits, fusion joins — and reactors use fission

Power reactors run on controlled FISSION (splitting uranium). FUSION (joining light nuclei) powers stars and is not yet a practical power source. Distractors swap these and also attach the wrong scientist (E = mc² is Einstein, not Rutherford/Bohr).

Reactor = CONTROLLED fission (a bomb is uncontrolled)

The reactor's whole point is keeping fission controlled and steady. An uncontrolled fission chain reaction is an atomic bomb. The exam answer for a reactor is always "controlled fission."

Penetration and ionising power run OPPOSITE ways

Gamma penetrates most but ionises least; alpha penetrates least (stopped by paper) but ionises most. Mixing up the two rankings is the classic radiation trap.

Pitchblende, not coal or limestone

Nuclear fuel comes from uranium ores such as pitchblende. Coal/petroleum are chemical (fossil) fuels, not nuclear. The exam answer for nuclear fuel mineral is pitchblende.

Quantum and Modern EM: X-rays, Semiconductors, Scattering

Learn this subtopic in the notes

Dimensions of Planck's constant — same as angular momentum

Dimensions of Planck's constant

[h] = \dfrac{[E]}{[f]} = \text{J}\cdot\text{s} = [\text{angular momentum}]

$h$ Planck's constant
$E$ energy (J)
$f$ frequency (Hz = s⁻¹)

X-rays — properties and uses

Statement about X-rays	True or false
Wavelength about 1 Å	True
Generated by bombarding a metal target with high-energy electrons	True
Used for radar systems because of their short wavelength	FALSE NDA 2023 — the false statement is that X-rays are used for radar. Radar uses long radio/microwaves, not X-rays.
Used to treat certain cancers	True

Everything about X-rays is true EXCEPT the radar claim. Radar = radio/microwave, not X-ray.

Semiconductors — p-type, n-type, and the I-V graph

Type	Majority charge carriers	Created by doping with
p-type	Holes (positive)	Trivalent impurity (e.g. boron)Q NDA 2017 — the majority charge carriers in a p-type semiconductor are holes.
n-type	Electrons (negative)	Pentavalent impurity (e.g. phosphorus)

p-type = holes (positive). n-type = electrons (negative). A plain wafer's I-V graph is a straight line through the origin.

Scattering phenomena — the Raman effect

Phenomenon	What happens
Raman effect	Scattered light's frequency CHANGES (inelastic scattering) NDA 2021 — light scattered with a changed frequency is the Raman effect.
Rayleigh scattering	Scattering with NO frequency change (elastic)
Photoelectric effect	Light ejects electrons from a metal — not scattering
Rutherford scattering	Alpha particles scatter off atomic nuclei

Frequency CHANGES = Raman. No change = Rayleigh. The other two are different phenomena entirely.

Common traps

X-rays for radar is the WRONG statement

Radar needs long wavelengths that reflect off aircraft and ships — radio waves and microwaves. X-rays have wavelengths far too short for radar. Any option pairing X-rays with radar is false.

h is angular momentum, not linear momentum or torque

J·s = angular momentum. Linear momentum is kg·m/s; torque is N·m = J (no extra second). Only angular momentum (and action) matches J·s.

p-type carriers are HOLES (positive), n-type are electrons

The letters track the carrier sign: p = positive (holes), n = negative (electrons). Distractors swap them. A plain wafer is still ohmic — linear I-V, not a diode curve.

Raman = frequency CHANGES; Rayleigh = no change

The defining feature of the Raman effect is a SHIFT in the scattered light's frequency. Rayleigh scattering leaves frequency unchanged. The wording "frequency is changed" points to Raman.

Scientists and Discoveries: Match the Pair

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Key modern-physics discoveries and their scientists

Scientist	Discovery / contribution
James Chadwick	Neutron
Albert Einstein	Photoelectric effect explanation; relativity (E = mc²)
Marie Curie	Radium (and polonium); radioactivity NDA 2021 — in the match list, only "Marie Curie : Radium" was correctly matched (Chadwick was wrongly paired with photoelectric effect, Einstein with neutron).
Ernest Rutherford	Atomic nucleus (alpha scattering)
J. J. Thomson	Electron (cathode rays)
Niels Bohr	Stable electron orbits (Bohr model)

The exam plants swaps: Chadwick is the NEUTRON (not photoelectric), Einstein is the PHOTOELECTRIC EFFECT (not the neutron), Curie is RADIUM.

LIGO — confirming gravitational waves and general relativity

Item	Fact
LIGO full form	Laser Interferometer Gravitational-wave Observatory
LIGO confirmed	Gravitational waves predicted by Einstein's General Theory of Relativity NDA 2024 — the LIGO experiment confirmed a prediction of the General Theory of Relativity.
LED full form	Light Emitting Diode (a semiconductor device)Q

LIGO detected gravitational waves and so confirmed General Relativity. LED is a Light Emitting Diode.

Common traps

Chadwick = neutron, Einstein = photoelectric effect

The favourite swap pairs Chadwick with the photoelectric effect and Einstein with the neutron — both wrong. Chadwick discovered the neutron; Einstein explained the photoelectric effect.

LIGO confirmed GENERAL relativity (via gravitational waves)

Gravitational waves are a prediction of the GENERAL theory of relativity (the one about gravity and spacetime), not the special theory. LIGO's detection confirmed general relativity.

Scientific Acronyms: Full Forms to Memorise

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Device and optics acronyms — LED, LASER, LCD

Acronym	Full form
LED	Light Emitting Diode NDA 2018 / 2021 — LED stands for Light Emitting Diode.
LASER	Light Amplification by Stimulated Emission of Radiation
LCD	Liquid Crystal Display
CFL	Compact Fluorescent Lamp

LED = Light Emitting Diode. Note LASER's expansion turns on "Stimulated Emission".

Big-science and research acronyms — LIGO, LASER, MASER

Acronym	Full form
LIGO	Laser Interferometer Gravitational-wave Observatory NDA 2019 — LIGO stands for Laser Interferometer Gravitational-wave Observatory.
MASER	Microwave Amplification by Stimulated Emission of Radiation
SONAR	Sound Navigation and Ranging
RADAR	Radio Detection and Ranging

LIGO opens with LASER and ends with OBSERVATORY. RADAR uses radio waves; SONAR uses sound.

Common traps

LED's D is DIODE, not Display

LED = Light Emitting DIODE (a semiconductor). LCD = Liquid Crystal DISPLAY. Do not let the similar look swap the D-words.

LIGO starts with LASER, not Light

The first word of LIGO is "Laser" (the interferometer fires laser beams), giving Laser Interferometer Gravitational-wave Observatory. Do not expand the L as "Light".

Modern Physics formulas

Photoelectric Effect: Light as Particles

The photon — light carries energy in discrete packets E = hf

Cutoff wavelength and the energy-voltage link

Who explained the photoelectric effect — Einstein and the Nobel Prize

Common traps

Atomic Structure: Models, Shells, and Energy

Bohr's model — electrons in stable orbits without radiating

Cathode rays — the discovery of the electron

Rutherford's alpha-scattering — the nucleus

Electron shells and ionisation energy — the fixed numbers

Common traps

Nuclear Physics: Fission, Fusion, and Reactors

Nuclear energy — fission, fusion, and E = mc²

The nuclear reactor — controlled fission and its parts

Nuclear fuel, measuring radioactivity, and radiation types

Common traps

Quantum and Modern EM: X-rays, Semiconductors, Scattering

Dimensions of Planck's constant — same as angular momentum

X-rays — properties and uses

Semiconductors — p-type, n-type, and the I-V graph

Scattering phenomena — the Raman effect

Common traps

Scientists and Discoveries: Match the Pair

Key modern-physics discoveries and their scientists

LIGO — confirming gravitational waves and general relativity

Common traps

Scientific Acronyms: Full Forms to Memorise

Device and optics acronyms — LED, LASER, LCD

Big-science and research acronyms — LIGO, LASER, MASER

Common traps

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