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.5.2 Energy Released in Fusion Reactions — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 39 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.

0%read

Lesson summary

E.5.2 Energy Released in Fusion Reactions — IB PHYSICS SL notes: Calculate the energy released in fusion from mass differences or binding energies and compare fusion with fission.The larger nucleus formed has a higher binding energy per nucleon than the original nuclei.There is a…

There is a mass defect between the original nuclei and the new nucleus
In the hot core of a star fusion begins with two protons forming deuterium
Alternative
Use atomic masses or nuclear masses consistently
With nuclear masses the mass defect is about 0.0265 u
The positrons annihilate with two electrons

Part 1 of 8Why fusion releases energy

The larger nucleus formed has a higher binding energy per nucleon than the original nuclei.

2There is a mass defect between the original nuclei and the new nucleus

There is a mass defect between the original nuclei and the new nucleus the difference in binding energy is released.

3Example

Example two deuterium nuclei fusing to helium-4: helium has about 28 MeV, the deuterons about 4 MeV, so about 24 MeV is released.

4In the hot core of a star fusion begins with two protons forming deuterium

In the hot core of a star fusion begins with two protons forming deuterium then helium forms and the star keeps burning.

Part 2 of 8Calculating the energy released

Calculating the energy released

Write the reaction and check that nucleon number and charge balance.

List the masses and find Δm = Σm_reactants − Σm_products.

Q (MeV) = Δm (u) × 931.5, or in joules Q = Δm c².

Calculating the energy released

Alternative

Q = Σ binding energy of products − Σ binding energy of reactants.
Free protons and neutrons have zero binding energy.

Use atomic masses or nuclear masses consistently

Use atomic masses or nuclear masses consistently so the electrons balance on both sides.

A positron emission step brings two extra electron masses into the balance.

Part 3 of 8Hydrogen to helium in the Sun

Hydrogen to helium in the Sun

Overall

4 ¹₁H gives ⁴₂He + 2e⁺ + 2 neutrinos.

With nuclear masses the mass defect is about 0.0265 u

With nuclear masses the mass defect is about 0.0265 u about 24.7 MeV.

The positrons annihilate with two electrons

The positrons annihilate with two electrons releasing a further 2 × 1.02 MeV, so the total is about 26.7 MeV.
Neutrinos escape with about 2% of the energy.

Using atomic masses, 4(1.007825 u) − 4.002603 u

0.028697 u — about 4.3 × 10^-12 J per reaction.

This is about 0.7% of the rest-mass energy of the hydrogen consumed.

Part 4 of 8Deuterium-tritium reaction

²₁H + ³₁H gives ⁴₂He + ¹₀n, releasing 17.6 MeV.

The neutron carries about 14.1 MeV and the helium nucleus about 3.5 MeV.

2It has the lowest ignition temperature, about 108 K

It has the lowest ignition temperature, about 108 K so it is the most promising fusion reaction on Earth.

3Deuterium is abundant in seawater

Deuterium is abundant in seawater tritium is radioactive and must be bred from lithium using the neutrons.
- (half-life 12.3 years)

The neutron's energy is captured as heat in a surrounding blanket.

Part 5 of 8Fusion compared with fission

Feature	Fusion	Fission
Energy per nucleon	About 3.5 to 6 MeV (hydrogen isotopes to helium)	About 0.85 MeV (uranium)
Energy per kilogram	About 6 × 10¹⁴ J for hydrogen to helium, roughly 8 times uranium-235	About 8 × 10¹³ J for uranium-235
Reason	Binding energy curve is steeper for light nuclei	Curve is shallow for heavy nuclei
Initial energy input	Greater	Smaller
Waste	Helium, not radioactive; neutrons activate the structure	Radioactive fission products

1Both reactions have products of slightly less mass than the reactants

Both reactions have products of slightly less mass than the reactants the mass defect equals the energy released.

2Fusion plasma cannot run away

Fusion plasma cannot run away if conditions fail the reaction simply stops.

Part 6 of 8Power of the Sun

Power of the Sun

The Sun radiates 3.83 × 10²⁶ W.

Mass lost per second

P / c² — about 4.3 × 10⁹ kg s^-1, roughly four million tonnes.

About 6 × 1011 kg of hydrogen fuses every second

About 6 × 1011 kg of hydrogen fuses every second a tiny fraction of the Sun's mass of 2.0 × 10³⁰ kg.

So the Sun can keep its output for billions of years.

Worked check

Worked check the reactions per second equal divided by energy per reaction.
- (power minus neutrino share)

Part 7 of 8Fusion power on Earth

Fusion power on Earth

Net power needs ignition temperature, high enough density and long enough confinement time (the Lawson criterion).

Magnetic confinement (tokamaks and stellarators)

Magnetic confinement (tokamaks and stellarators) holds hot plasma away from the walls with strong magnetic fields.

Inertial confinement

Inertial confinement lasers compress a tiny fuel pellet.

Difficulties

Difficulties heating plasma to 10⁸ K, preventing instabilities and building walls that withstand neutron bombardment.

Energy appears as kinetic energy of the products

Energy appears as kinetic energy of the products shared by momentum conservation, so the lighter product carries the larger share.

Part 8 of 8More from the specification

Transitions in nuclear energy levels

Transitions in nuclear energy levels mass differences converted into radiant energy correspond to quantum steps between discrete nuclear energy levels.

Stellar Fusion and Main Sequence Equilibrium

Main sequence stars generate energy by fusing hydrogen into helium in their cores;
- hydrostatic equilibrium is maintained when outward radiation and thermal pressure balance inward gravitational contraction.

Luminosity and Stefan-Boltzmann Law

A star's total radiant power output (luminosity L) depends on its surface radius R and surface temperature T according to the Stefan-Boltzmann equation L = 4πR²σT⁴.

Stellar Absorption Spectra and Spectral Classes

As stellar light passes through cooler outer atmospheres, specific wavelengths are absorbed,
producing distinctive dark absorption lines that classify stars into spectral types.
- (O, B, A, F, G, K, M)

Stellar Parallax and Cosmic Distance

Stellar parallax determines the distance d to nearby stars by measuring the apparent angular shift p against background stars as Earth orbits the Sun,
where distance in parsecs equals d = 1 / p.

Stable main-sequence star

An equilibrium state where inward gravitational collapse is counteracted by outward thermal pressure generated from sustained nuclear fusion.

White dwarf

Small, hot, dense core left by a low-mass star.

Surface temperature

Effective temperature of the star's radiating surface.

Energy level

A discrete energy an electron in an atom can have

Continuous spectrum

Spectrum with no gaps between the regions.

Spectrum

Range of colours in white light.

Luminosity

The total power of radiation emitted by a star.

Absorption

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

Parallax

Apparent shift between objects caused by viewing from different positions

Distance

Total length of path travelled, a scalar.

Photon

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

Radius

Distance from the centre to the circular path.

Wavelength

Distance between a point on one wave and the same point on the next wave

Key terms

Term	Meaning
Q value	Energy released in a nuclear reaction.
D-T reaction	Fusion of deuterium and tritium into helium and a neutron, releasing 17.6 MeV.
Tokamak	Magnetic confinement device with a doughnut-shaped plasma.
Lawson criterion	Condition on density, temperature and confinement time for net energy gain.
Ignition	Fusion that sustains itself with no external heating.
Mass defect	Mass lost when nuclei fuse, equivalent to the energy released.

Avoid these mistakes

Using nuclear and atomic masses together without balancing the electrons.

Thinking fusion releases less energy per kilogram than fission — it releases more.

Forgetting that neutrinos carry away some of the energy in the proton-proton chain.

Giving the D-T energy as 17.6 J instead of 17.6 MeV.

Believing the Sun's mass is being used up rapidly — it loses a tiny fraction.

Last updated: 18 October 2026