Atomic Structure
The atomic structure is the fundamental concept in chemistry and physics, explaining the composition of matter. It involves understanding the arrangement and properties of subatomic particles that make up an atom.
Subatomic Particles
An atom consists of three main subatomic particles:
- Protons: Positively charged particles found in the nucleus. They have a relative charge of +1 and a mass of approximately 1 atomic mass unit (amu).
- Neutrons: Neutral particles found in the nucleus. They have no charge (0) and a mass of approximately 1 amu.
- Electrons: Negatively charged particles orbiting the nucleus in energy levels or electron shells. They have a relative charge of -1 and negligible mass compared to protons and neutrons.
Numerical Example 1: Subatomic Particles
An atom of carbon has 6 protons, 6 neutrons, and 6 electrons. Identify the atomic number, mass number, and charge of the atom.
Solution:
Atomic Number (Z): The number of protons in an atom is equal to its atomic number. For carbon, Z = 6.
Mass Number (A): The total number of protons and neutrons in an atom is its mass number. For carbon, A = 6 + 6 = 12.
Charge (Q): The charge of an atom is the difference between the number of protons and electrons. For carbon, Q = 6 - 6 = 0 (neutral atom).
Therefore, the atomic number of carbon is 6, the mass number is 12, and it is a neutral atom.
Electronic Configuration
Electronic configuration is the distribution of electrons in different energy levels or shells around the nucleus of an atom. The electronic configuration of an element is crucial in determining its chemical properties.
Numerical Example 2: Electronic Configuration
Write the electronic configuration of oxygen (O) and calcium (Ca) using the notation (1s² 2s² 2p⁶ ...).
Solution:
Oxygen (O) Electronic Configuration: 1s² 2s² 2p⁴
Calcium (Ca) Electronic Configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²
Therefore, the electronic configuration of oxygen is 1s² 2s² 2p⁴ and calcium is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s².
Isotopes and Atomic Number
Isotopes are atoms of the same element with different numbers of neutrons. They have the same atomic number but different mass numbers.
Numerical Example 3: Isotopes and Atomic Number
Hydrogen has three isotopes: protium (H-1), deuterium (H-2), and tritium (H-3). Identify their atomic numbers and mass numbers.
Solution:
Protium (H-1): Atomic Number (Z) = 1, Mass Number (A) = 1
Deuterium (H-2): Atomic Number (Z) = 1, Mass Number (A) = 2
Tritium (H-3): Atomic Number (Z) = 1, Mass Number (A) = 3
Therefore, the atomic number of all hydrogen isotopes is 1, but their mass numbers are 1, 2, and 3, respectively.
Periodic Table
The periodic table is a tabular arrangement of elements based on their atomic numbers and chemical properties. It is organized into periods (rows) and groups (columns).
Bohr's Model of the Atom
Bohr proposed a model of the atom where electrons orbit the nucleus in discrete energy levels or shells. Electrons can absorb or emit energy when transitioning between energy levels, explaining the line spectra of elements.
Numerical Example 4: Bohr's Model of the Atom
Calculate the energy of an electron in the n = 3 energy level of a hydrogen atom.
Solution:
Energy of an Electron (E): E = -2.18 × 10⁻¹⁸ J / n²
E = -2.18 × 10⁻¹⁸ J / 3² = -2.18 × 10⁻¹⁸ J / 9 ≈ -2.42 × 10⁻¹⁹ J
Therefore, the energy of an electron in the n = 3 energy level of a hydrogen atom is approximately -2.42 × 10⁻¹⁹ joules (J).
Quantum Mechanical Model
The quantum mechanical model describes the behavior of electrons as both particles and waves. It involves the use of wave functions (orbitals) to represent the probability of finding electrons in different regions around the nucleus.
Quantum Numbers
Quantum numbers are set of four numbers that describe the properties and characteristics of electrons in an atom. They are used to define the electron's energy, orbital shape, orientation, and spin within an atom.
1. Principal Quantum Number (n)
The principal quantum number (n) determines the main energy level or shell in which an electron resides. It denotes the average distance of the electron from the nucleus and the energy of the electron.
2. Angular Momentum Quantum Number (l)
The angular momentum quantum number (l) defines the shape of the orbital in which an electron is located. It represents the subshell (s, p, d, f) and the shape of the electron's cloud around the nucleus.
3. Magnetic Quantum Number (ml)
The magnetic quantum number (ml) describes the orientation of the orbital in space. It indicates the specific spatial orientation of an orbital within a subshell.
4. Spin Quantum Number (ms)
The spin quantum number (ms) describes the spin of an electron. It can have two possible values: +1/2 (spin-up) or -1/2 (spin-down).
Numerical Example 1: Quantum Numbers
For an electron in an atom, given n = 3, l = 1, ml = 0, and ms = +1/2, determine the quantum numbers and the location of the electron.
Solution:
The quantum numbers for the electron are:
- Principal Quantum Number (n) = 3
- Angular Momentum Quantum Number (l) = 1
- Magnetic Quantum Number (ml) = 0
- Spin Quantum Number (ms) = +1/2
The electron is located in the 3p orbital of the atom.
Different Proposals of Atomic Structures
1. Dalton's Atomic Model
Dalton proposed the first atomic model in the early 19th century. According to his model:
- Atoms are indivisible and indestructible.
- All atoms of an element are identical in mass and properties.
- Atoms combine in simple whole-number ratios to form compounds.
- Chemical reactions involve the rearrangement of atoms.
2. Thomson's Plum Pudding Model
Thomson proposed the Plum Pudding Model in the late 19th century. According to his model:
- Atoms are composed of a positively charged sphere with negatively charged electrons embedded in it.
- The atom is electrically neutral overall.
- It was later disproved by the results of the gold foil experiment by Rutherford.
3. Rutherford's Nuclear Model
Rutherford proposed the Nuclear Model in the early 20th century. According to his model:
- The atom has a dense, positively charged nucleus at its center, containing protons.
- Electrons orbit the nucleus at a considerable distance.
- Most of the atom's mass is concentrated in the nucleus.
4. Bohr's Atomic Model
Bohr proposed the Atomic Model in the early 20th century. According to his model:
- Electrons orbit the nucleus in fixed energy levels or shells.
- Electrons can jump between energy levels by absorbing or emitting energy in the form of photons.
- Bohr's model successfully explained the spectral lines of hydrogen.
Numerical Example 2: Bohr's Model
Calculate the energy of an electron in the n = 2 energy level of a hydrogen atom using Bohr's model.
Solution:
Energy of an Electron (E): E = -13.6 eV / n²
E = -13.6 eV / 2² = -13.6 eV / 4 = -3.4 eV
Therefore, the energy of an electron in the n = 2 energy level of a hydrogen atom is -3.4 electron volts (eV).
5. Quantum Mechanical Model
The Quantum Mechanical Model is the most modern and widely accepted atomic model. It combines wave mechanics and the concept of orbitals to describe the behavior of electrons in atoms.
Hydrogen Spectrum
The hydrogen spectrum is the set of spectral lines produced when hydrogen gas is excited and emits light. It played a crucial role in the development of quantum mechanics and our understanding of atomic structure.
Emission and Absorption Spectrum
When hydrogen gas is subjected to an external energy source (such as an electric discharge or high temperature), the electrons in hydrogen atoms get excited to higher energy levels. When these excited electrons return to lower energy levels, they release energy in the form of light. This emitted light consists of a series of discrete wavelengths or colors, forming an emission spectrum.
On the other hand, when white light or continuous radiation passes through a cooler hydrogen gas, some wavelengths of light are absorbed by the hydrogen atoms, resulting in an absorption spectrum. The absorption spectrum appears as dark lines on a continuous spectrum.
Balmer Series
The Balmer series is a set of spectral lines in the hydrogen emission spectrum that corresponds to transitions of electrons from higher energy levels (n ≥ 3) to the second energy level (n = 2).
Numerical Example: Balmer Series
Calculate the wavelength of the spectral line in the Balmer series when an electron transitions from the n = 4 energy level to the n = 2 energy level in a hydrogen atom.
Solution:
The Balmer series formula is given by:
1 / λ = R_H (1 - 1 / n²)
where λ is the wavelength, R_H is the Rydberg constant (approximately 1.097 × 10⁷ m⁻¹), and n is the principal quantum number.
For the n = 4 to n = 2 transition:
1 / λ = 1.097 × 10⁷ (1 - 1 / 4² - 1 / 2²) = 1.097 × 10⁷ (1 - 1 / 16 - 1 / 4) = 1.097 × 10⁷ (1 - 1/16 - 1/4) = 1.097 × 10⁷ × (11/16) = 7.339 × 10⁶ m⁻¹
λ ≈ 1 / (7.339 × 10⁶ m⁻¹) ≈ 1360 nm
Therefore, the wavelength of the spectral line in the Balmer series is approximately 1360 nanometers (nm).
Lyman Series
The Lyman series is another set of spectral lines in the hydrogen emission spectrum that corresponds to transitions of electrons from higher energy levels (n ≥ 2) to the first energy level (n = 1).
Paschen Series
The Paschen series is a set of spectral lines in the hydrogen emission spectrum that corresponds to transitions of electrons from higher energy levels (n ≥ 4) to the third energy level (n = 3).
Bracket Series
The Bracket series is a set of spectral lines in the hydrogen emission spectrum that corresponds to transitions of electrons from higher energy levels (n ≥ 5) to the fourth energy level (n = 4).
Pfund Series
The Pfund series is a set of spectral lines in the hydrogen emission spectrum that corresponds to transitions of electrons from higher energy levels (n ≥ 6) to the fifth energy level (n = 5).