ARAT INTERNATIONAL SCHOOLWEEK 6 - NUCLEUS
DEFINITION OF NUCLEUS
The nucleus is the small, dense center of an atom where most of the atom’s mass is concentrated.
It was discovered through the gold foil experiment conducted by Ernest Rutherford in 1911. The nucleus is positively charged and occupies only a tiny fraction of the volume of the atom but contains nearly all its mass.
CONSTITUENTS OF THE NUCLEUS
The nucleus is made up of two fundamental subatomic particles:
1. Protons
o Positively charged particles.
o Each proton carries a charge of +1.6 × 10⁻¹⁹ C.
o The number of protons determines the element and is called the proton number or atomic number (Z).
2. Neutrons
o Electrically neutral particles.
o Similar mass to protons but no charge.
o Neutrons contribute to the mass of the atom and influence nuclear stability.
Together, protons and neutrons are called nucleons.
NUCLEON NUMBER, PROTON NUMBER, ISOTOPES, AND NUCLIDES
1. Nucleon Number (Mass Number, A):
o Total number of protons and neutrons in the nucleus.
o A = Z + N
Where:
A = Nucleon number
Z = Number of protons (proton number)
N = Number of neutrons
2. Proton Number (Z):
o Number of protons in the nucleus.
o Defines the chemical identity of an atom (e.g., hydrogen has Z = 1).
3. Isotopes:
o Atoms of the same element (same proton number) but different nucleon numbers.
o Example:
* Hydrogen isotopes:
* Protium (¹H), Deuterium (²H), Tritium (³H)
4. Nuclides:
o A nuclide is a specific isotope of an element characterized by its proton and neutron numbers.
o Represented as:
ÀXz
Example: 614C¹⁴ represents a carbon nuclide with 6 protons and 8 neutrons.
NUCLEAR PROPERTIES
1. Mass Defect (Δm):
o The difference between the sum of the masses of individual nucleons and the actual mass of the nucleus.
o Indicates that some mass has been converted into energy that binds the nucleons together.
2. Binding Energy (BE):
o The energy required to split a nucleus into its individual protons and neutrons.
o It reflects the stability of the nucleus.
o Calculated using Einstein’s mass-energy equivalence:
E = Δm∙c²
Where:
E = Binding energy (in joules or MeV)
Δm = Mass defect (in kg or u)
c = Speed of light (3 × 10⁸ m/s)
3. Nuclear Stability:
o Stable nuclei have a balanced ratio of protons to neutrons
o Too many or too few neutrons can lead to radioactive decay.
4. 'half life': The half life of a substance is defined as the time taken for half of the atoms in any given substance to decay
T=0.692/ λ
T = half life
⋋ = decay constant
NUCLEAR FISSION AND FUSION
Nuclear Fission: This is a process in which a nuclear bombardment of the nucleus of a heavy nuclide by particles such as a neutrons, resulting in splitting of the nucleus into two smaller nuclei with the release of large amount of energy.
Example:
23592U + 10n → 14857La + 8535Br + 310n + Energy Release
o A heavy nucleus (e.g., uranium-235) splits into two lighter nuclei with the release
of a large amount of energy and free neutrons.
o Used in nuclear reactors and atomic bombs.
o Chain reaction can occur if released neutrons initiate further fissions.
Nuclear Fusion:
o Two light nuclei (e.g., hydrogen isotopes) combine to form a heavier nucleus.
o Releases even more energy than fission.
o Occurs naturally in stars, including the sun.
o Requires extremely high temperature and pressure.
COMPONENT OF THE NUCLEAR REACTOR
- nuclear fuels
- nuclear moderator
- control rods
- Reactor coolants
- The turbine
- Cooling towers.
FUNCTION OF NUCLEAR FUELS
- The fuel help to supply the needed energy would power the nuclear reactor .
Function nuclear moderators
- They are used to slow down fast moving neutron which can cause further fission. Examples include Graphite
function of controls rods
- they are used to absorb neutron which can lead to further fission. Examples are boron, cadmium e.t.c
Function of reactor coolants.
They are used to carry th heat produced by fission to external boiler and turbine where it is transformed into electricity, examples are liquid sodium, lead e.t.c
Function of turbine
- it transfer to heat from coolant to electricity
Function of cooling towers
-They are used to dump the excess heat that cannot be converted to energy due to the laws of thermodynamics.
USES AND HAZARDS OF NUCLEAR ENERGY
Applications:
1. Medicine:
o Radiation therapy for cancer treatment.
o Radioisotopes used in diagnostic imaging (e.g., iodine-131 for thyroid imaging).
2. Industry:
o Non-destructive testing of materials using radioactive tracers.
o Sterilization of medical equipment.
3. Power Generation:
o Nuclear reactors generate electricity using controlled fission.
Example: Pressurized Water Reactor (PWR), Boiling Water Reactor (BWR)
Hazards:
* Exposure to high doses of radiation can cause cancer, genetic mutations, and acute radiation sickness.
* Radioactive waste disposal poses long-term environmental and health risks.
* Nuclear accidents (e.g., Chernobyl, Fukushima) can have catastrophic consequences.
Einstein’s Mass-Energy Equivalence and Binding Energy Calculation
The equation:
E=Δm⋅c²
is used to calculate binding energy when the mass defect is known. Binding energy per nucleon is an important measure of nuclear stability.
Example 2:
A radioactive isotope of Americium (Am - 241) decays into nucleus of Neptunium (Np - 237) and an alpha (α) particle as shown in the nuclear equation below.
24195Am → 237CNp + ba∝
Determine the values of a, b and c.
Solution:
(b) 241
95(Am )→ 237cNp +ba∝
Recall that b
a∝ =4
2(He) 241
95(Am) → 237cNp +4
2He
(ii)95 = c+2; c = 93
(i) Number of neutrons = 241 - 95 = 146
Example 2: a nucleus has a mass defect Δm=0.0025 u, convert to kg:
Solution
Δm = 0.0025×1.66×10−²⁷kg
= 4.15×10−³⁰ kg
E = 4.15×10−³⁰×(3×108)²
= 3.735×10−¹³
Alternatively, use 1 u = 931 MeV for direct energy conversion:
E = 0.0025×931= 2.33 MeV
Example 3:
In a nuclear reaction, the mass defect is 2.0 x 10-⁶ g. Calculate the energy released, given that the velocity of light is 3.0 x 10
8 ms-¹.
Solution:
E = ?Δm = 2.0 x 10-⁶g
= 2.0 x 10-⁹kg;
c = 3 x 10⁸ ms-1
E = Δmc²
= 2.0 x 10-⁹ x (3 x 10⁸)²
= 2.0 x 10-⁹ x 9 x 10¹⁶
= 18 x 10⁷J
= 1.8 x 10⁸ J
Evaluation (WAEC/NECO Past Questions)
1. (WAEC 2019 Q6): Explain the difference between mass number and atomic number of an element.
2. (NECO 2021 Q9): State two differences between nuclear fission and fusion.
3. (WAEC 2022 Q3): A helium nucleus has a mass defect of 0.0304 u. Calculate its binding energy. (1 u = 931 MeV)
4. (WAEC 2018 Q10): Give one medical and one industrial application of nuclear energy.
5. (NECO 2020 Q4): What is an isotope? Give two examples of isotopes of hydrogen.
Assignment
1. Define the following terms: nuclide, isotope, binding energy.
2. Differentiate between nuclear fission and nuclear fusion with one example each.
3. Calculate the binding energy in MeV of a lithium nucleus that has a mass defect of 0.035u.
4. Mention two advantages and two disadvantages of using nuclear energy in power generation.
5. Give one example each of the use of nuclear radiation in:
o Medicine
o Industry
o Agriculture