Atomic Structure notes

Discovery of the Proton and Positive Rays

The proton is a positively charged subatomic particle present in the nucleus of an atom. Its charge is equal in magnitude to the charge of an electron but opposite in sign. A proton has a relative mass of approximately 1 atomic mass unit.

Positive rays were observed by E. Goldstein using a discharge tube containing gas at low pressure. These rays passed through holes in the cathode, so they were called canal rays or anode rays. Their particles came from the gas molecules present in the discharge tube and depended on the gas used.

• A proton has a charge of +1.6022 x 10^-19 C.
• The mass of a proton is approximately 1.673 x 10^-27 kg.
• Canal rays travel from the anode towards the cathode and pass through holes in the cathode.
• Cathode rays travel from the cathode to the anode.
• Canal rays are produced from gas molecules in the discharge tube.
• The nucleus of a helium atom contains two protons and two neutrons.
• A helium nucleus with two protons, two neutrons, and a charge of 2e is called an alpha particle.
• The sum of protons and neutrons in an atom is called its mass number or nucleon number.

Electron, Atomic Number, Mass Number and Isotopes

An atom contains electrons, protons, and neutrons. Electrons occupy regions around the nucleus, while protons and neutrons are present in the nucleus. In a neutral atom, the number of electrons is equal to the number of protons.

The atomic number identifies an element. The mass number gives the total number of nucleons. Isotopes have the same atomic number but different mass numbers because they contain different numbers of neutrons.

• Atomic number, Z, equals the number of protons in an atom.
• For a neutral atom, number of protons equals number of electrons.
• Mass number, A, equals number of protons plus number of neutrons.
• Number of neutrons equals A minus Z.
• An increase in atomic number occurs during beta emission because a neutron changes into a proton and an electron is emitted.
• During alpha emission, atomic number decreases by 2 and mass number decreases by 4.
• The electron has a charge of -1.6022 x 10^-19 C.
• The charge to mass ratio, e/m, of an electron is 1.7588 x 10^11 C kg^-1, and its mass is approximately 9.1095 x 10^-28 g.

Planck's Quantum Theory

Classical physics considered energy to be continuous. Planck proposed that atoms and molecules absorb or emit energy in small packets called quanta. The energy of one quantum depends on the frequency of radiation.

The energy change of an electron is not continuous. An electron can absorb or release only a definite amount of energy when it moves between allowed energy levels. The energy is released or absorbed as electromagnetic radiation.

• One quantum is the smallest packet of energy that can be absorbed or emitted by an atom.
• The energy of a quantum is given by E = hν.
• In this equation, E is energy, h is Planck's constant, and ν is frequency.
• Planck's constant is 6.626 x 10^-34 J s.
• Frequency and energy are directly proportional.
• Since c = λν, the energy can also be written as E = hc/λ.
• Higher frequency radiation has greater energy.
• An electron absorbs energy when it moves from a lower energy level to a higher energy level and emits energy when it returns to a lower level.

Bohr Model and Hydrogen Spectrum

Bohr proposed that the electron in a hydrogen atom moves around the nucleus in certain permitted circular orbits. These orbits have fixed energies. An electron in an allowed orbit does not continuously lose energy, so it does not radiate energy while remaining in that orbit.

When an electron jumps from one energy level to another, radiation is absorbed or emitted. The line spectrum of hydrogen is produced because only particular energy differences are possible. Hydrogen orbit radii are of the order of 10^-11 m.

• The principal quantum number n identifies the main energy level or shell.
• The allowed angular momentum of an electron is mvr = nh/2π.
• For the first orbit, n = 1; for the second orbit, n = 2, and so on.
• An electron in a particular permitted orbit does not radiate energy.
• A jump from a higher level to a lower level emits a photon.
• A jump from a lower level to a higher level absorbs a photon.
• The Lyman series is produced when electrons fall to n = 1 and lies in the ultraviolet region.
• The Balmer series is produced when electrons fall to n = 2 and lies in the visible region.
• An electron jumping from the fourth orbit to the first orbit produces a line in the Lyman series.
• The Paschen series ends at n = 3 and lies in the infrared region.

Quantum Numbers

Quantum numbers describe the position, energy, shape, and orientation of an electron in an atom. Three quantum numbers are obtained from the solution of Schrödinger's wave equation. These are principal, azimuthal, and magnetic quantum numbers. The spin quantum number is related to the spinning motion of the electron and is not obtained by solving Schrödinger's wave equation.

A permissible set of quantum numbers must follow the allowed relationships between n, l, m, and s. The spin quantum number has only two possible values.

• The principal quantum number, n, gives the main shell and has values 1, 2, 3, 4 and so on.
• For a given value of n, the azimuthal quantum number l has values from 0 to n - 1.
• The azimuthal quantum number l describes the subshell and shape of an orbital.
• The values l = 0, 1, 2, 3 represent s, p, d, and f subshells respectively.
• The magnetic quantum number m or ml gives the orientation of an orbital and has values from -l to +l.
• For n = 2, the possible values of l are 0 and 1. For l = 1, m values are -1, 0, and +1.
• The spin quantum number s or ms has values +1/2 and -1/2.
• The set n = 3, l = 3, m = 1, s = -1/2 is not permissible because l cannot be equal to n.
• The quantum number s is not obtained by solving Schrödinger's wave equation.
• The maximum number of electrons in a subshell is 2(2l + 1).

Orbitals and Their Shapes

An orbital is a three-dimensional region around the nucleus where the probability of finding an electron is high. An orbital is not a fixed circular path. The shape of an orbital is determined by the azimuthal quantum number, l.

The wave function may have regions where its value or electron probability is zero. Such regions are called nodes. The electron density between the 1s and 2s orbitals is zero because a radial node exists between them.

• An s orbital has a spherical shape and one orbital is present in each s subshell.
• A p subshell contains three p orbitals: px, py, and pz.
• The three p orbitals have dumbbell shapes and are oriented along the x, y, and z axes.
• A p subshell can accommodate a maximum of 6 electrons.
• A d subshell contains five orbitals and can accommodate 10 electrons.
• An f subshell contains seven orbitals and can accommodate 14 electrons.
• The shape of an orbital is determined by l, while its orientation is determined by m.
• A pi bond is formed by sideways overlap of parallel p orbitals.
• The region between the 1s and 2s orbitals has zero electron density.

Subshells, Energy Levels and Shielding Effect

The energy of an electron depends on the shell and subshell in which it is present. In multi-electron atoms, subshells in the same principal shell may have different energies. Generally, the energy order follows the Aufbau sequence.

Inner electrons reduce the attraction between the nucleus and outer electrons. This effect is called shielding or screening effect. Because of shielding, outer electrons experience a lower effective nuclear charge than the actual nuclear charge.

The removal of an electron requires ionization energy. Electrons held more strongly by the nucleus require more energy to remove. The effective nuclear charge, distance from the nucleus, and shielding effect all affect this energy.

• Shielding effect is also called screening effect.
• Inner-shell electrons shield outer-shell electrons from the attraction of the nucleus.
• Greater shielding generally makes the removal of an outer electron easier.
• Across a period, effective nuclear charge generally increases because proton number increases while shielding changes only slightly.
• Down a group, atomic size and shielding generally increase.
• In chlorine, the 3d orbitals are higher in energy than the 3s and 3p orbitals.
• For a neutral atom, an electron in a more stable, lower-energy arrangement requires more energy to remove.
• Ionization energy is the energy required to remove the most loosely held electron from an isolated gaseous atom.
• A positive ion generally holds its remaining electrons more strongly than the corresponding neutral atom.

Electronic Configuration and Rules of Filling

Electronic configuration shows the distribution of electrons in shells and subshells. Electrons occupy orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund's rule. These rules explain the ground-state arrangements of atoms.

The Aufbau principle states that electrons enter orbitals in order of increasing energy. The Pauli exclusion principle states that no two electrons in an atom can have the same four quantum numbers. Hund's rule states that orbitals of equal energy are singly occupied before pairing occurs.

• The common filling order is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, and 7p.
• An s subshell holds 2 electrons, a p subshell holds 6, a d subshell holds 10, and an f subshell holds 14.
• The maximum number of electrons in a shell is 2n^2.
• The maximum number of orbitals in a subshell is 2l + 1.
• The notation 1s2 means that two electrons occupy the 1s subshell.
• The configuration 1s2 2s1 is the ground-state configuration of lithium.
• A configuration with an electron promoted to a higher subshell than required in the ground state is called an excited-state configuration.
• The configuration 1s2 2s1 2p1x 2p1y 2p1z for an atom having six electrons represents an excited state.
• Chromium has the exceptional ground-state configuration [Ar] 3d5 4s1.
• Copper has the stable ground-state configuration [Ar] 3d10 4s1.
• Chromium and copper show exceptions because half-filled d5 and completely filled d10 subshells have extra stability.