Basic ideas about nucleus
Basic Ideas About Nucleus
The nucleus is the central part of an atom, where most of the atom's mass is concentrated. It was discovered by Ernest Rutherford in 1911 through his famous gold foil experiment. The nucleus is composed of two types of subatomic particles: protons and neutrons, collectively known as nucleons.
Composition of the Nucleus
- Protons: Positively charged particles with a charge of +1e, where e is the elementary charge ($e = 1.602 \times 10^{-19}$ coulombs).
- Neutrons: Neutral particles with no charge. Neutrons and protons have nearly the same mass, approximately $1.675 \times 10^{-27}$ kilograms, which is about 1836 times the mass of an electron.
The number of protons in the nucleus is called the atomic number (Z), and it determines the identity of the element. The total number of protons and neutrons is the mass number (A).
Properties of the Nucleus
- Size: The nucleus is extremely small compared to the size of the atom. Its radius (R) can be estimated using the empirical formula: $R = R_0 A^{1/3}$, where $R_0$ is a constant approximately equal to $1.2 \times 10^{-15}$ meters and A is the mass number.
- Density: The nuclear density is extremely high since the nucleus occupies a very small volume. It is roughly $2.3 \times 10^{17}$ kg/m³, which is approximately constant for all nuclei.
- Binding Energy: The energy required to disassemble a nucleus into its constituent protons and neutrons is called the binding energy. It is a measure of the stability of a nucleus. The binding energy per nucleon generally increases with atomic number up to iron (Fe), after which it slowly decreases.
Nuclear Forces
The nucleus stays intact due to the strong nuclear force, which is a short-range force that acts between all nucleons. It is much stronger than the electromagnetic force that causes repulsion between positively charged protons.
Nuclear Reactions
Nuclear reactions involve changes in the nucleus and can release or absorb significant amounts of energy. There are two main types of nuclear reactions:
- Fission: The splitting of a heavy nucleus into two or more lighter nuclei, accompanied by the release of energy.
- Fusion: The combining of two light nuclei to form a heavier nucleus, also releasing energy.
Differences Between Nucleus and Atom
| Property | Nucleus | Atom |
|---|---|---|
| Size | Very small (10^-15 meters) | Much larger (10^-10 meters) |
| Mass | Contains most of the atom's mass | Contains all of the atom's mass |
| Charge | Positive due to protons | Neutral overall |
| Composition | Protons and neutrons | Nucleus and electrons |
| Forces | Strong nuclear force | Electromagnetic force |
Example: Binding Energy Calculation
The binding energy (BE) can be calculated using Einstein's mass-energy equivalence formula, $E = mc^2$, where $m$ is the mass defect and $c$ is the speed of light ($3 \times 10^8$ m/s).
For example, consider a helium-4 nucleus with 2 protons and 2 neutrons. The mass of the helium-4 nucleus is less than the sum of the masses of 2 free protons and 2 free neutrons. This difference in mass is the mass defect.
Let's say the mass defect ($\Delta m$) is $0.0304$ atomic mass units (u). To convert this to kilograms, we use the conversion factor $1 u = 1.660539 \times 10^{-27}$ kg. Then, the mass defect in kilograms is $\Delta m = 0.0304 \times 1.660539 \times 10^{-27}$ kg.
The binding energy is then calculated as:
$$ BE = \Delta m \times c^2 $$ $$ BE = 0.0304 \times 1.660539 \times 10^{-27} \text{ kg} \times (3 \times 10^8 \text{ m/s})^2 $$ $$ BE = 4.533 \times 10^{-12} \text{ J} $$
To express the binding energy in electron volts (eV), we use the conversion factor $1 \text{ J} = 6.242 \times 10^{18} \text{ eV}$:
$$ BE = 4.533 \times 10^{-12} \text{ J} \times 6.242 \times 10^{18} \text{ eV/J} $$ $$ BE = 28.3 \text{ MeV} $$
Therefore, the binding energy of a helium-4 nucleus is approximately 28.3 MeV.
Understanding the basic ideas about the nucleus is crucial for studying nuclear physics, nuclear chemistry, and various applications such as nuclear energy, medical imaging, and radiation therapy.