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.3.10 Binding Energy per Nucleon Curve — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 27 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.3.10 Binding Energy per Nucleon Curve — IB PHYSICS SL notes: Interpret the curve of binding energy per nucleon against nucleon number to explain fusion, fission and nuclear stability.Binding energy per nucleon = the binding energy of a nucleus divided by its number of nucleons.…

Rising side
Surface nucleons have fewer neighbours
Falling side
The product has a higher binding energy per nucleon
The gradient is steep at low A
Fusion needs a very large initial energy input

Part 1 of 8Reading the curve

1Binding energy per nucleon

Binding energy per nucleon the binding energy of a nucleus divided by its number of nucleons.

A higher value means more energy is needed to separate the nucleons, so the nucleus is more stable.

The graph plots binding energy per nucleon (MeV) against nucleon number A.

3Low A

Low A binding energy per nucleon is lower and rises steeply; light nuclei tend to be stable when N = Z.

4High A

High A values are higher but fall slowly as A increases; the heaviest nuclei are the least stable.

5Peak

Peak iron-56 (A = 56) has the highest value, about 8.8 MeV, so it is the most stable nucleus.
The final value for uranium is about 7.6 MeV per nucleon.

6Anomalies

Anomalies helium-4 is exceptionally stable and sits high above the trend.
Carbon-12 and oxygen-16 behave like three and four helium nuclei bound together.

Part 2 of 8Why the curve rises then falls

1Rising side

Rising side each added nucleon is attracted by more neighbours through the short-range strong force.

2Surface nucleons have fewer neighbours

Surface nucleons have fewer neighbours which lowers the average binding in small nuclei.

3Falling side

Falling side the strong force saturates because it only reaches nearby nucleons.
The electrostatic repulsion between protons has a long range and grows with Z.
In heavy nuclei the repulsion begins to dominate, causing instability.

Part 3 of 8Fusion

Fusion

Fusion two light nuclei (A below 56) combine into a heavier nucleus.

The product has a higher binding energy per nucleon

The product has a higher binding energy per nucleon so energy is released.

The gradient is steep at low A

The gradient is steep at low A so fusion releases more energy per kilogram of fuel than fission.

Fusion needs a very large initial energy input

Fusion needs a very large initial energy input to overcome electrostatic repulsion between the nuclei.

Stars fuse elements up to iron

Stars fuse elements up to iron heavier elements form in other processes such as supernovae.

Part 4 of 8Fission

1Fission

Fission a heavy unstable nucleus (A above 56) splits into two smaller nuclei.

2The fragments have a higher binding energy per nucleon

The fragments have a higher binding energy per nucleon so energy is released.

3The gradient is shallow at high A

The gradient is shallow at high A so the gain is only about 1 MeV per nucleon.
This gives about 200 MeV per fission of uranium-235.

4Energy released Q

Energy released Q total binding energy of products − total binding energy of reactants.

Part 5 of 8Comparing fusion and fission

Feature	Fusion	Fission
Process	Light nuclei join	Heavy nucleus splits
Nuclei involved	A below 56	A above 56
Energy per kilogram	Much greater	Smaller
Initial energy needed	Greater	Smaller

1Similarity

Similarity the total mass of the products is slightly less than that of the reactants.
The mass defect is equivalent to the binding energy released, Δm = Q/c².

2No energy can be extracted by fusing or splitting iron

No energy can be extracted by fusing or splitting iron it is at the peak.

Part 6 of 8Using the curve for energy calculations

Using the curve for energy calculations

Read the binding energy per nucleon of each nuclide from the graph.

Multiply each value by its nucleon number to get total binding energy.

Subtract the total for the reactants from the total for the products.

1Only nuclei are included

Only nuclei are included free neutrons and protons have zero binding energy.

2Estimate for U-235 fission

Estimate for U-235 fission fragments at about 8.5 MeV and U-235 at about 7.6 MeV give a gain of about 0.9 × 235, roughly 210 MeV.

Part 7 of 8Strong nuclear force

Strong nuclear force

A nucleus has repulsive electric forces between protons

A nucleus has repulsive electric forces between protons and negligible gravitational attraction.

An attractive force stronger than electric repulsion must act between all nucleons

the strong nuclear force.
It acts between quarks, so it holds protons and neutrons together.

Range

Range repulsive below about 0.5 fm, attractive up to about 3.0 fm, and zero beyond that.
The attraction is greatest near 1.0 fm, a typical nucleon separation.

It does not depend on charge

It does not depend on charge so it is about equal for proton-proton, neutron-neutron and proton-neutron pairs.

Electrostatic repulsion has a longer range

Electrostatic repulsion has a longer range but is weaker than the strong force between 0.5 and 3.0 fm.

Part 8 of 8More from the specification

Long stellar fusion years

Long stellar fusion years ascending the nuclear binding curve toward iron-56 releases the energy powering main sequence stars over billions of years.

Binding Energy per Nucleon Stability Curve

The curve of binding energy per nucleon reaches a maximum near iron-56;
- light nuclei release energy via fusion to form more tightly bound products,
while heavy unstable isotope nuclei release energy via fission toward greater stability.

Alpha and Gamma Modes of Radioactive Decay

An unstable radioactive isotope undergoing alpha decay emits an alpha particle,
- (helium-4 nucleus)
reducing mass number by 4 and atomic number by 2; excess nuclear excitation energy is subsequently released as high-frequency gamma radiation.

Radioactive Sample Decay Law

The activity of a radioactive sample follows exponential decay N(t) = N₀ e^(-λt),
where the decay constant λ is inversely related to half-life by t½ = ln(2) / λ.

Binding Energy per Nucleon Stability Curve

The curve of binding energy per nucleon reaches a maximum near iron-56;
- light nuclei release energy via fusion to form more tightly bound products,
while heavy unstable isotope nuclei release energy via fission toward greater stability.

Alpha and Gamma Modes of Radioactive Decay

An unstable radioactive isotope undergoing alpha decay emits an alpha particle,
- (helium-4 nucleus)
reducing mass number by 4 and atomic number by 2; excess nuclear excitation energy is subsequently released as high-frequency gamma radiation.

Radioactive Sample Decay Law

The activity of a radioactive sample follows exponential decay N(t) = N₀ e^(-λt),
where the decay constant λ is inversely related to half-life by t½ = ln(2) / λ.

Alpha particle

Helium nucleus, charge +2.

Alpha decay

Loss of 2 protons and 2 neutrons.

Ionising radiation

Radiation with enough energy to remove electrons from atoms

Penetrating power

How far radiation travels through a material.

Nuclear notation

Symbol showing mass number and atomic number.

Beta-plus decay

Proton changes to a neutron with emission of a positron and a neutrino.

Decay equation

An equation in nuclide notation with balanced nucleon and proton numbers.

Radiation

Transfer by electromagnetic waves, requiring no medium

Radioactive

Describes a nucleus that decays spontaneously and randomly.

Half-life

Time for half the nuclei of an isotope to decay.

Isotope

Atom of the same element with a different number of neutrons.

Isotopes

Nuclei with the same proton number but different neutron numbers.

Source

Reservoir at T_H providing heat Q_H

Background radiation

Radiation that is always present in the environment.

Radioactive decay

Natural process in which unstable nuclei release energy.

Key terms

Term	Meaning
Binding energy per nucleon	Total binding energy divided by nucleon number.
Iron-56	Nucleus near the peak of the curve, the most tightly bound.
Fusion	Joining of light nuclei into a heavier one.
Fission	Splitting of a heavy nucleus into lighter ones.
Strong nuclear force	Attractive force between nucleons acting over about 0.5 to 3.0 fm.
Saturation	The strong force acts only between neighbouring nucleons.
Q value	Energy released by a nuclear reaction.

Avoid these mistakes

Believing the curve peaks at uranium or helium — the maximum is near iron-56 and nickel-62.

Thinking energy is released when moving to lower binding energy per nucleon — it is released when it increases.

Saying fission releases more energy per kilogram than fusion — fusion gives more per unit mass.

Starting the curve at A = 0 — there is no nucleus with no nucleons.

Forgetting that free nucleons have zero binding energy.

Last updated: 18 October 2026