كيف يحسب الرقم الهيدروجيني pH للمحاليل؟ How to calculate pH and pOH?

يحسب الرقم الهيدروجيني بالعلاقة: pH = -log[H⁺]، وللمحاليل المائية عند 25°C: pH + pOH = 14. إذا كان pH 7 فالمحلول قاعدي. [الصيغة الرمزية الموزونة: pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴]

Theme E — Nuclear and Quantum Physics

Theme E — Nuclear and Quantum Physics — IB Physics HL Revision Notes & Topical Questions

10 min read 11 parts Lesson 1 of 45 Unit quiz

📚 IB Physics HL Hub / Topical Revision

Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution

pH = -log[H⁺]  |  pOH = -log[OH⁻]  |  pH + pOH = 14  |  [H⁺][OH⁻] = 10⁻¹⁴

Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14

Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.

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Lesson summary

Theme E — Nuclear and Quantum Physics — IB PHYSICS HL notes: Summarise atomic structure, spectra, the photoelectric effect, de Broglie waves, radioactive decay, fission, fusion and the physics of stars for IB Physics HL.Nuclear model — positively charged protons and neutral neutr…

Nucleon number
Strong nuclear force
Nuclear radius
Line spectra
Photon energy
Planck constant

Part 1 of 8Atomic structure, nuclear force and spectra

Atomic structure, nuclear force and spectra

Nuclear model

Nuclear model positively charged protons and neutral neutrons sit in a tiny nucleus surrounded by electrons

Nucleon number

Nucleon number the total number of protons and neutrons

Strong nuclear force

Strong nuclear force a short-range attraction between nucleons

Stability

Stability light stable nuclei have about equal neutron and proton numbers
Heavier stable nuclei need extra neutrons to offset growing proton repulsion
Nuclei away from the stability line decay

Quarks

Quarks deep inelastic scattering of high-energy electrons revealed quarks inside nucleons

Nuclear radius

Nuclear radius electron diffraction can be used to measure it

HL extras

HL extras the Bohr model of hydrogen, nuclear radius, closest approach and nuclear density

Line spectra

Line spectra each element absorbs and emits light at characteristic wavelengths

Origin

Origin electrons make transitions between discrete energy levels

Photon energy

E = hf equals the energy-level difference

Planck constant

Planck constant h = 6.63 × 10⁻³⁴ J s

Part 2 of 8The photoelectric effect

The photoelectric effect

Einstein's explanation

Einstein's explanation conservation of energy for one photon and one electron, hf = Φ + K_max

Work function Φ

Work function Φ the minimum energy needed to remove an electron from the surface

Maximum kinetic energy

K_max = ½mv_max²

Range of energies

Range of energies surface electrons lose only Φ and deeper electrons lose more, so emitted electrons have energies up to K_max

Stopping potential

V_s is the reverse p.d. that just stops the most energetic electrons, eV_s = K_max

Part 3 of 8Wave properties of particles

Wave properties of particles

de Broglie wavelength

de Broglie wavelength particles have wave properties with λ = h/p

Evidence

Evidence electron diffraction

Double slit with single electrons

Double slit with single electrons the pattern builds up gradually and each electron is detected as a whole
The wavefunction passes through both slits

Probability

Probability the probability of detection is proportional to the square of the wavefunction amplitude

Uncertainty principle

Uncertainty principle a fundamental limit and not just a result of clumsy measurement

Duality

Duality both wave and particle aspects always belong to the same object

Part 4 of 8Types of radioactive decay

Types of radioactive decay

Radioactive decay

Radioactive decay emission of particles or radiation from an unstable nucleus, which becomes a daughter nuclide or a lower-energy state

Ionising

Ionising the radiation is hazardous to tissue and detectable, for example in a Geiger–Müller tube

Emission	Nature	Change	Notes
Alpha	Helium-4 nucleus, charge +2e	A falls by 4 and Z by 2	Strongly ionising, least penetrating
Beta minus	Electron	Neutron becomes proton, Z rises by 1, antineutrino emitted	Stopped by a few mm of aluminium
Beta plus	Positron	Proton becomes neutron, Z falls by 1, neutrino emitted	Continuous energy spectrum
Gamma	High-energy photon	No change in A or Z	Energy equals the difference between nuclear levels

Types of radioactive decay

Beta energies

Beta energies a continuous range from zero to a maximum, which was evidence for the neutrino

Gamma energies

Gamma energies discrete and far larger than atomic electron levels, so convert MeV to joules when finding wavelength

Part 5 of 8Fission, reactors and waste

Fission

Fission a heavy nucleus splits after capturing a thermal neutron, releasing more neutrons
- (A much greater than 60)

Chain reaction

Chain reaction the neutrons cause further fissions
A minimum critical mass is needed to sustain it

Energy

Energy the products are nearer the peak of the binding energy per nucleon curve,
so ΔE = Δmc², about 200 MeV per fission, mostly as kinetic energy of fragments

Moderator

Moderator slows neutrons to thermal speeds

Control rods

Control rods neutron-absorbing material that regulates the rate

Coolant

Coolant carries thermal energy from the core to a heat exchanger where steam drives turbines and generators

Shielding

Shielding thick concrete and steel absorb neutrons and gamma radiation

Spent fuel

Spent fuel generates heat and radioactive waste

High-level waste

High-level waste a small share of the volume but most of the radioactivity

Half-life

Half-life a long half-life means lower activity per atom but longer storage
Waste is not harmless after one half-life because half the activity remains

Reprocessing

Reprocessing it recovers fuel but does not remove the waste

Part 6 of 8Fusion

Feature	Fission	Fusion
Process	Heavy nucleus splits	Light nuclei join
Nuclei involved	A much greater than 60	A much less than 60
Conditions	Thermal neutrons	Very high temperature and density
Energy per unit mass	Lower	Higher
Where	Nuclear reactors	Stars

Condition

Condition very high temperature is needed to overcome electrostatic repulsion so nuclei approach close enough for the strong force to act

D–T reaction

D–T reaction releases 17.6 MeV

Tokamak

Tokamak confines plasma magnetically

Lawson criterion

Lawson criterion sets the density, temperature and confinement time for net gain, and ignition occurs when fusion sustains itself

Part 7 of 8Stars and distances

Star formation

Star formation a cloud collapses, converting gravitational potential energy to thermal energy
Angular momentum flattens the cloud into a disc

Main sequence

Main sequence when the core reaches about 10⁷ K hydrogen fusion starts and outward pressure balances gravity in hydrostatic equilibrium
A hotter core expands and cools, so it is self-regulating

Mass ranges

Mass ranges below 0.08 solar masses a brown dwarf, 0.08 to 8 solar masses Sun-like, above 8 solar masses massive, short-lived and more luminous

Later stages

Later stages helium fuses when the core contracts (3 ⁴₂He → ¹²₆C at about 10⁸ K)
Massive stars fuse up to iron-56, which has the maximum binding energy per nucleon

Heavy elements

Heavy elements formed by neutron capture in supernovae and mergers

End states

End states a star much more massive than the Sun ends as a neutron star or black hole after a supernova

H–R diagram

H–R diagram red giants are more luminous than main-sequence stars of the same temperature because of larger area, L = σAT⁴
What the symbols mean: L = luminosity, the total power emitted (W) · σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ · r = radius of the star (m) · A = surface area (m²) · T = surface temperature (K)
White dwarfs are hot but dim at the bottom left

Parallax

Parallax the parallax angle p is half the apparent shift over six months, d = 1/p in parsecs

Units

1 pc = 3.09 × 10¹⁶ m, 1 ly = 9.46 × 10¹⁵ m, 1 AU = 1.50 × 10¹¹ m and 1 arc-second = 1/3600 degree

Example value

Example value a star with p = 0.10 arcsecond is 10 pc away

Part 8 of 8More from the specification

Rutherford Alpha Scattering Experiment

Directing alpha particles at thin gold foil demonstrated that most particles pass straight through while a small fraction deflect at large angles, proving atoms contain a tiny, dense, positively charged nucleus.

Quantized Atomic Orbits

Electrons orbit atomic nuclei only in discrete standing wave states where orbital circumference equals an integer number of de Broglie wavelengths, avoiding continuous radiative energy loss.

Atomic Absorption Spectrum

When white light traverses a cool atomic vapor, electrons absorb specific photon frequencies to transition to higher energy levels,
producing dark absorption lines across the continuous spectrum.

Spectral Emission and Energy Levels

The characteristic discrete wavelengths of atomic emission and absorption spectra provide empirical proof of quantized electron energy levels in atoms.

Absorption

The conversion of wave energy to internal energy of the medium.

Rutherford scattering

Scattering of charged particles by a nucleus through electrostatic repulsion alone.

Absorption spectrum

A continuous spectrum crossed by dark lines where a cool gas absorbed specific wavelengths.

∆E

∆E hf = E2 − E1

What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10⁻³⁴ J s) · f = frequency (Hz)

Key terms

Term	Meaning
Half-life	The time for half the radioactive nuclei, or the activity, to decay.
Activity	The number of decays per second of a sample, measured in becquerel.
Work function	The minimum energy needed to remove an electron from a metal surface.
de Broglie wavelength	The wavelength associated with a particle, λ = h/p.
Chain reaction	A reaction in which neutrons released by fission cause further fission events.
Hydrostatic equilibrium	The balance between gravity inwards and gas and radiation pressure outwards in a star.
Parallax	Half the apparent angular shift of a star over six months, used for d = 1/p.
Binding energy	The energy required to separate a nucleus completely into its nucleons.

Avoid these mistakes

Assuming beta particles have discrete energies — their spectrum is continuous, supporting the neutrino.

Thinking waste is harmless after one half-life — only half of the activity has gone.

Saying the mass of a sample halves each half-life — only the number of undecayed nuclei halves.

Confusing nuclear energy levels with atomic ones — nuclear transitions involve far larger energies.

Saying light is a wave on some occasions and a particle on others.

Last updated: 15 October 2026