The Bohr Model 2: Quantum Mechanics

Explain the historical development of the Quantum Mechanical Model of the atom.   Describe the quantum arrangement of electrons in an atom. Include: energy level, shape, and orbital. Additional KEY Terms Principal quantum number (n)

de Broglie (1924) – developed an equation that predicts wave qualities for all matter. If waves of light could contain photon-particles, could matter have wave properties? Suggests orbits are fixed because electrons (as a wave) could only move as strict standing wavelength

The famous “double-slit” experiment proved the “wave-particle duality” of matter (click the TV link below)

Think - trying to catch a frog in the dark with a flashlight… Problems: World is 3-dimensional Bohr’s math failed to explain all spectra Matter also has wave properties Heisenberg (1925) - it is impossible to know precisely the velocity and position of a particle at the same time – Heisenberg Uncertainty Principle Think - trying to catch a frog in the dark with a flashlight…

Schrödinger (1926) – developed a wave equation that describes the energies and behaviour of subatomic particles. Determines the probability of finding an electron in a 3-D volume of space around the nucleus. At this point, scientists couldn’t really figure matter out experimentally, so they turned to math and computers…

Each energy level's boundary is the area of electron location 90% of the time

principle quantum number (n) Bohr’s orbits are now called: principle quantum number (n) The (n) number indirectly describes the size and energy requirements of an orbit

The probable location of every electron is now described by a set of 4 quantum numbers: principal (n) distance from the nucleus 2. orbital angular momentum (l) shape of orbital 3. magnetic (m) orientation in 3D space 4. spin angular momentum (s) spin of the election

s p d f There are four shapes appearing in this order: Principle quantum numbers (n) contain many places of probable electron location – shapes (l) There are four shapes appearing in this order: s p d f Each shape (l) can be made of multiple orbitals (m) that occupy the axes of 3D space (x, y, z) Each orbital holds two spinning electrons (s)

Like stadium seating, the further from the stage the more “sections” of seating NUCLEUS n = 1 s n = 2 s p n = 3 s p d Notice: number of shapes (l) equal the principal quantum number (n) for that level

“s” shape (sphere) – 1 orbital (m) Only one “way” to place a sphere in 3D space

“p” shape (dumbbell) – 3 orbitals (m) Three orientations for placing a dumbbell in 3D space

“d” shape (cloverleaf) – 5 orbital orientations (m) “f” shape (indeterminate) – 7 orbital orientations (m)

Remember – each orbital (m) holds two spinning electrons (s) Principal Level (n) Shapes (l) Total Orbitals 1 s 1s = 1 2 s,p 1s+3p = 4 3 s,p,d 1s+3p+5d = 9 4 s,p,d,f 1s+3p+5d+7f = 16 n n shapes n2 orbitals Remember – each orbital (m) holds two spinning electrons (s)

n = 3 1s 2s 2p 3s 3p 3d n = 2 n = 1 OLD way NEW way

CAN YOU / HAVE YOU? Explain the historical development of the Quantum Mechanical Model of the atom.   Describe the quantum arrangement of electrons in an atom. Include: energy level, shape, and orbital. Additional KEY Terms Principal quantum number (n)