Electronic structure of the atom
- 1. ELECTRONIC STRUCTURE OF THE ATOM Prepared by: Eden C. Sanchez
- 2. Explain Heisenberg’s Uncertainty Principle Describe how atomic orbitals arise from the Schrodinger equation Relate orbital shapes to electron density distribution Qualitatively sketch the orbital shapes Interpret the information obtained from a set of four quantum numbers Objectives
- 3. Assign the correct set of quantum numbers for an electron Objectives
- 4. a. Heisenberg’s Uncertainty Principle b. Schrodinger Equation c. Wave function d. Electron probability density e. Atomic orbital f. Principal quantum number g. Angular momentum quantum number Keywords
- 5. Keywords h. Magnetic quantum number i. Spin quantum number j. Shell k. Subshell
- 6. HEISENBERG’S UNCERTAINTY PRINCIPLE formulated by Werner Heisenberg, a German physicist “the position of a particle and its momentum cannot be simultaneously measured with arbitrarily high precision” In other words, it is not possible to measure the exact position and the exact momentum of a particle at the same time.
- 7. Mathematically, this is stated as: where "x is the uncertainty in position, "p is the uncertainty in momentum, and h is Planck’s constant
- 8. The Bohr model violates Heisenberg’s Uncertainty Principle. Electrons do not go around the nucleus in well-defined orbits. Otherwise, we will be able to determine the exact position and momentum of the electron in the atom at the same time. A better model is needed to fully describe the atom.
- 9. SCHRODINGER EQUATION In 1926, Erwin Schrodinger, an Austrian physicist, formulated a mathematical equation that describes the behavior and energies of submicroscopic particles. The Schrodinger equation incorporates particle behavior and wave behavior, treating the electron as a standing wave.
- 10. SCHRODINGER EQUATION The solution to the Schrodinger equation is a wave function called ψ (psi). The wave functions are also called atomic orbitals (as distinguished from the Bohr orbits). Aside from the wave functions, energies are also obtained from solving the equation.
- 11. The wave function itself has no physical meaning. However, the probability of finding the electron in a particular volume element in space is proportional to ψ2. In wave theory, the intensity of light is proportional to the square of the amplitude of the wave or ψ2. Similarly, the most likely place to find the particle is where the value of ψ2 is greatest.
- 12. The Schrodinger equation began a new field in physics and chemistry referred to as quantum mechanics or wave mechanics. The Schrodinger equation can be solved exactly for the hydrogen atom but not for atoms with more than one electron. For many-electron atoms, approximation methods are used to solve the Schrodinger equation.
- 13. THE QUANTUM MECHANICAL DESCRIPTION OF THE HYDROGEN ATOM It is not possible to pinpoint the exact location of the electron in an atom but ψ2 gives the region where it can most probably be found. The electron density gives the probability that the electron will be found in a particular region of an atom.
- 14. THE QUANTUM MECHANICAL DESCRIPTION OF THE HYDROGEN ATOM representation of the electron density distribution around the nucleus in the hydrogen atom
- 15. THE QUANTUM MECHANICAL DESCRIPTION OF THE HYDROGEN ATOM The darker the shade, the higher the probability of finding the electron in that region. the probability distribution is spherical ψ is the solution to the Schrodinger equation. It is also referred to as an atomic orbital.
- 16. THE QUANTUM MECHANICAL DESCRIPTION OF THE HYDROGEN ATOM When we say that the electron is in an atomic orbital, we mean that it is described by a wave function, ψ, and that the probability of locating the electron is given by the square of the wave function associated with that orbital. The atomic orbital has a characteristic energy as well as a characteristic electron density distribution. This electron density distribution in three-dimensions gives the shape of the atomic orbital.
- 17. In the mathematical solution of the Schrodinger equation, three quantum numbers are obtained. These are the principal quantum number (n), the angular quantum number, (ℓ) ,and the magnetic quantum number (ml). They describe the atomic orbitals. A fourth quantum number, the spin quantum number (ms) completes the description of the electrons in the atoms. The QUANTUM NUMBERS
- 18. a. Determines the energy of an orbital b. Determines the orbital size c. Is related to the average distance of the electron from the nucleus in a particular orbital; the larger the n value, the farther the average distance of the electron from the nucleus d. Can have the values: n = 1, 2, 3, … e. Orbitals with the same n are said to be in the same shell. Principal Quantum Number (n)
- 19. a. Describes the “shape” of the orbitals b. Can have the following values: ℓ = 0, 1, 2, up to n-1. Examples n value ℓ value 1 0 2 0, 1 3 0, 1, 2 Angular Momentum Quantum Number (ℓ)
- 20. c. Orbitals with the same n and ℓ values belong to the same subshell. d. It is usually designated by letters s, p, d, f, … which have a historical origin from spectral lines. The designations are as follows Angular Momentum Quantum Number (ℓ)
- 21. The s, p, d, f designations of the orbitals refer to sharp, principal, diffuse, and fundamental lines in emission spectra.
- 22. a. Describes the orientation of the orbital in space b. Can have the values: - ℓ, (-ℓ + 1), … 0, … (+ ℓ - 1), + ℓ Magnetic Quantum Number (ml)
- 23. a. The first three quantum numbers describe the energy, shape and orientation of orbitals. The 4th quantum number refers to two different spin orientations of electrons in a specified orbital. Electron Spin Quantum Number (ms)
- 24. b. When lines of the hydrogen spectrum are examined at very high resolution, they are found to be closely spaced doublets and called as the Zeeman effect. This splitting is called fine structure, and was one of the first experimental evidences for electron spin. The direct observation of the electron's intrinsic angular momentum was achieved in the Stern–Gerlach experiment. Electron Spin Quantum Number (ms)
- 25. Electron Spin Quantum Number (ms) c. Uhlenbeck, Goudsmit, and Kronig (1925) introduced the idea of the self-rotation of the electron. The spin orientations are called "spin-up" or "spin-down" and is assigned the number ms = ½ ms = -½, respectively.
- 26. d. The spin property of an electron would give rise to magnetic moment, which was a requisite for the fourth quantum number. The electrons are paired such that one spins upward and one downward, neutralizing the effect of their spin on the action of the atom as a whole. But in the valence shell of atoms where there is a single electron whose spin remains unbalanced, the unbalanced spin Electron Spin Quantum Number (ms)
- 27. creates spin magnetic moment, making the electron act like a very small magnet. The four quantum numbers compose the numbers that describe the electron in an atom. The quantum numbers shall be in the order: energy level (n), sub-level or orbital type (ℓ), the orientation of the orbital specified in ℓ (mℓ), and the orientation of the spin of the electron (ms). It is written in the order (n, ℓ, mℓ, ms). Electron Spin Quantum Number (ms)
- 28. 1. An electron is found in the first energy level. What is the allowed set of quantum numbers for this electron? 2. What is the total number of orbitals associated with the principal quantum number n=1? 3. What is the total number of orbitals associated with the principal quantum number n=2? Example
- 29. 4. What is the total number of orbitals associated with the principal quantum number n=3? 5. List the values of n, ℓ , mℓ for an orbital in the 4d subshell.
- 30. What are the shapes of the atomic orbitals? • Strictly speaking, an orbital does not have a definite shape because the wave function extends to infinity. However, while the electron can be found anywhere, there are regions where the probability of finding it is much higher. The Representations of the Shapes of Atomic Orbitals
- 31. The Representations of the Shapes of Atomic Orbitals The electron density distribution of a 1s electron around the nucleus.
- 32. The p orbitals starts when n =2 for which ℓ has a value of 1 and mℓ has values -1, 0, +1. There are three 2p orbitals: 2px, 2py, 2pz indicating the axes along which they are oriented. For the p orbitals, the electron probability density is not spherically symmetric but has a double teardrop shape, or a dumbbell shape. The greatest probability of finding the electron is within the two lobes of the dumbbell region; The Representations of the Shapes of Atomic Orbitals
- 33. it has zero probability along the nodal planes found in the axes. All three 2p orbitals are identical in shape and energy but differ in orientation. The Representations of the Shapes of Atomic Orbitals
- 34. The d orbitals occur for the first time when n = 3. The angular function in these cases possesses two angular (or planar) nodes. Four of the orbitals have the same basic shapes except for the orientation with respect to the axes. The wave functions exhibit positive and negative lobes along the axes and shows zero probability of finding the electron at the origin. The Representations of the Shapes of Atomic Orbitals
- 35. The fifth wave function, dx2 , has a similar shape with that of the p-orbital with a donut-shape region along the x-axis.