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

E.5 Fusion and Stars — IB Physics HL Revision Notes & Topical Questions

5 min read 13 parts Lesson 37 of 45 1 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

E.5 Fusion and Stars — IB PHYSICS HL notes: Explain fusion and the energy it releases, the life cycle of stars, the H–R diagram, stellar spectra, parallax and stellar radii.Definition — the joining of two small nuclei to produce a larger nucleusProton fusion — 11H + 11H → 21H + e…

Proton–proton chain
Mass defect
Overall hydrogen burning
Kinetic energy
Short range
Temperature

Section 1 of 13Fusion reactions

Definition

Definition the joining of two small nuclei to produce a larger nucleus

Proton fusion

¹₁H + ¹₁H → ²₁H + e⁺ + neutrino, where one proton becomes a neutron by β⁺ decay

In stars

In stars four hydrogen nuclei fuse to form a helium nucleus, releasing a huge amount of energy and giving radiation pressure that prevents collapse

On Earth

On Earth the D–T reaction ²₁H + ³₁H → ⁴₂He + ¹₀n

Mass

Mass the helium nucleus has less mass than its separate nucleons, so energy is released per unit mass of fuel

Proton–proton chain

Proton–proton chain a series of reactions turning four protons into one helium nucleus

Section 2 of 13Energy released in fusion

Cause

Cause the larger nucleus has a higher binding energy per nucleon than the original nuclei

Mass defect

Mass defect the difference between the original nuclei and the new nucleus is the energy released, E = Δmc²
What the symbols mean: E = energy (J) · m or Δm = mass (change) (kg) · c = 3.00 × 10⁸ m s⁻¹

Example

Example two deuterium nuclei fusing to helium (about 28 MeV) release about 24 MeV
- (about 4 MeV total binding energy)

Overall hydrogen burning

Overall hydrogen burning the mass defect for four hydrogen-1 nuclei forming helium-4 gives the energy per reaction

Neutrinos

Neutrinos they carry away a small fraction of the energy

Power

Power the mass fused per second follows from the luminosity divided by the energy per reaction

Section 3 of 13Conditions for fusion

Kinetic energy

Kinetic energy nuclei need enough to overcome the electrostatic repulsion between protons

Short range

Short range the strong force acts only over a very short range, so nuclei must get very close

Temperature

Temperature very high, of the scale of 100 million kelvin

Density and pressure

Density and pressure very high

Where

Where in the core of a star or accelerated in a particle accelerator

Radiation pressure

Radiation pressure the momentum of gamma photons produces an outward pressure

Section 4 of 13Equilibrium of a star

Balance

Balance outward radiation and gas pressure balance the inward gravitational force

Self-regulation

Self-regulation if the temperature rises, pressure rises and the star expands
If it falls, the pressure falls and the star contracts

Stable

Stable as long as the forces are balanced the star remains stable

Gas pressure

Gas pressure it increases as gravitational collapse raises the temperature and decreases the volume

Section 5 of 13Star formation and low-mass stars

Nebula

Nebula a giant cloud of hydrogen gas and dust
Gravitational attraction forms denser clumps in a gravitational collapse

Protostar

Protostar collisions raise the temperature so the gas heats up and glows
It is detected in infrared and continues to attract gas and dust

Main sequence

Main sequence hydrogen fusion begins at millions of kelvin and the forces balance
About 90% of stars are here, with masses from 10% to 200 times the Sun

The Sun

The Sun it has been on the main sequence for 4.6 billion years and will stay for about 6.5 billion more

Red giant

Red giant core hydrogen runs out, fusion continues in a shell and the core contracts and heats until helium fuses
The outer layers expand and cool

Planetary nebula

Planetary nebula the carbon–oxygen core is not hot enough for further fusion and the outer layers are ejected

White dwarf

White dwarf the remaining hot, dense core

Section 6 of 13Massive stars

Red supergiant

Red supergiant formed like a red giant but with successive core and shell burning up to iron

Supernova

Supernova the iron core collapses and the outer shell is blown out in an explosion

Neutron star

Neutron star the collapsed neutron core can remain intact

Black hole

Black hole if the remnant core exceeds about 3 solar masses the pressure is so great that it collapses further

Iron

Iron it has the highest binding energy per nucleon so further fusion absorbs energy

Section 7 of 13The Hertzsprung–Russell diagram

1Axes

Axes luminosity on the y-axis from dim to bright, and surface temperature on the x-axis decreasing from left (hot) to right (cool)
- (relative to the Sun)

2Main sequence

Main sequence a diagonal band in which luminosity increases with surface temperature

3Red giants and supergiants

Red giants and supergiants above the main sequence, cooler but luminous because they are much larger
Supergiants are above giants

4White dwarfs

White dwarfs below and to the left, hot but dim, so much smaller

5Content

Content the diagram shows stars in stable phases only
Black holes cannot be seen

Section 8 of 13Stellar spectra

Continuous spectrum

Continuous spectrum all wavelengths, from the hot dense core of a star

Emission line spectrum

Emission line spectrum discrete coloured lines on a black background from hot low-pressure gas

Absorption line spectrum

Absorption line spectrum dark lines on a continuous spectrum when light passes through a cool low-pressure gas
The dark lines match the emission lines of the same element

Stars

Stars photons from the core pass through gas in the outer atmosphere, so stars show absorption line spectra

Composition

Composition each element has a unique pattern of lines, so stars' elements can be identified
The Sun's dark lines match hydrogen (486.3 nm, 656.5 nm) and helium (587.7 nm)

Surface temperature

Surface temperature stars approximate black-body radiators
A shorter peak wavelength means a hotter star, as hot stars are blue-white and cool stars red

Wien's law

λ_maxT = 2.9 × 10⁻³ m K

Section 9 of 13Distances and parallax

Astronomical unit

Astronomical unit the mean distance from the centre of the Earth to the centre of the Sun, 1.50 × 10¹¹ m

Light-year

Light-year the distance light travels in one year, 9.46 × 10¹⁵ m

Parsec

Parsec the distance giving a parallax angle of 1 arc-second with a baseline of 1 AU, 3.09 × 10¹⁶ m (3.26 ly)

Arc-second

1/3600 degree

Stellar parallax

Stellar parallax the apparent shift in position of a nearby star against distant stars when viewed six months apart

Equation

Equation tan p = 1 AU/d which for small angles gives p = 1 AU/d
In arc-seconds and parsecs, p = 1/d

Limit

Limit it is accurate for distances up to about 100 pc

Section 10 of 13Stellar radii

1Step 1

Step 1 use Wien's law to find the surface temperature from the peak wavelength

2Step 2

Step 2 use the inverse square law for flux to find the luminosity from the flux and distance

3Step 3

Step 3 use the Stefan–Boltzmann law L = 4πr²σT⁴ to find the radius

4Red giants

Red giants large radii, such as Betelgeuse at about 1000 times the Sun's radius

Section 11 of 13More from the specification

Stellar Nucleosynthesis in Massive Stars

A massive star fuses hydrogen into helium in its core,
and in subsequent evolutionary stages progresses to fusing heavier elements like carbon, oxygen, neon,
and silicon in concentric shells until forming an iron-56 core.

Hydrostatic Equilibrium and Radiation Pressure

Throughout main sequence stages, a star maintains hydrostatic equilibrium balancing inward gravitational contraction against outward gas pressure and radiation pressure produced by thermonuclear fusion.

Quantized Energy Levels and Stellar Spectra

Outer stellar atmospheric gases absorb specific photon wavelengths corresponding to discrete electronic energy levels in atoms,
producing characteristic dark absorption lines in stellar spectra that reveal composition and temperature.

Supernova Collapse and Stellar Remnants

When nuclear fusion ceases in an iron core, a massive star undergoes rapid gravitational collapse resulting in a Type II supernova, leaving behind an ultra-dense neutron star or black hole.

Energy level

A discrete energy an electron in an atom can have

Section 12 of 13Key terms

Term	Meaning
Nuclear fusion	The joining of two small nuclei to produce a larger nucleus.
Hydrostatic equilibrium	The balance between gravity inwards and gas and radiation pressure outwards in a star.
Protostar	A hot glowing ball of gas formed by gravitational collapse of a nebula.
Main sequence	The stable hydrogen-burning stage that is the long diagonal band on the H–R diagram.
Red giant	A large cool luminous star formed when core hydrogen runs out.
Parallax	The apparent shift of a nearby star against distant stars as the Earth orbits the Sun.
Parsec	The distance at which a star has a parallax angle of one arc-second.
Luminosity	The total power radiated by a star.

Section 13 of 13Exam technique

Thinking a star is stable because there is no fusion — stability needs a balance of outward pressure and gravity.

Plotting temperature increasing to the right on an H–R diagram — it increases to the left.

Saying all stars become black holes — it depends on the mass of the remnant core.

Using parallax angle in degrees in d = 1/p — it must be in arc-seconds.

Thinking fusion releases energy for all nuclei — it does so only for nuclei lighter than iron.

Last updated: 15 October 2026