Chapter 30 Atomic Physics

Properties of Atoms Atoms are stable and electrically neutral. Atoms have chemical properties which allow them to combine with other atoms. Atoms emit and absorb electromagnetic radiation with discrete energy and momentum. Early experiments showed that most of the mass of an atom was associated with positive charge. Atoms have angular momentum and magnetism.

Thompson’s Model for the Atom J.J. Thompson’s plum pudding model consists of a sphere of positive charge with electrons embedded inside. Electron Positive pudding Thompson’s plum pudding This model would explain that most of the mass was positive charge and that the atom was electrically neutral. The size of the atom (10-10 m) prevented direct confirmation.

Rutherford’s Experiment The Thompson model was abandoned in 1911 when Rutherford bombarded a thin metal foil with a stream of positively charged alpha particles. Rutherford Scattering Exp. Gold foil Screen Alpha source Most particles pass right through the foil, but a few are scattered in a backward direction.

The Nucleus of an Atom If electrons were distributed uniformly, particles would pass straight through an atom. Rutherford proposed an atom that is open space with positive charge concentrated in a very dense nucleus. Gold foil Screen Alpha scattering + - Electrons must orbit at a distance in order not to be attracted into the nucleus of atom.

Radius of Hydrogen atom Electron Orbits Consider the planetary model for electrons which move in a circle around the positive nucleus. The figure below is for the hydrogen atom. FC + - Nucleus e- r Coulomb’s law: Centripetal FC: Radius of Hydrogen atom

Failure of Classical Model When an electron is acceler-ated by the central force, it must radiate energy. v + - Nucleus e- The loss of energy should cause the velocity v to de-crease, sending the electron crashing into the nucleus. This does NOT happen and the Rutherford atom fails.

Atomic Spectra Earlier, we learned that objects continually emit and absorb electromagnetic radiation. In an emission spectrum, light is separated into characteristic wavelengths. Emission Spectrum l2 l1 Gas Absorption Spectrum In an absorption spectrum, a gas absorbs certain wave lengths, which identify the element.

The Bohr Atom Atomic spectra indicate that atoms emit or absorb energy in discrete amounts. In 1913, Neils Bohr explained that classical theory did not apply to the Rutherford atom. + Electron orbits e- An electron can only have certain orbits and the atom must have definite energy levels which are analogous to standing waves.

Wave Analysis of Orbits Stable orbits exist for integral multiples of de Broglie wavelengths. n = 4 + Electron orbits e- 2pr = nl n = 1,2,3, … Recalling that angular momentum is mvr, we write:

The Bohr Atom + The Bohr atom Energy levels, n An electron can have only those orbits in which its angular momentum is: Bohr’s postulate: When an electron changes from one orbit to another, it gains or loses energy equal to the difference in energy between initial and final levels.

Bohr’s Atom and Radiation Emission Absorption When an electron drops to a lower level, radiation is emitted; when radiation is absorbed, the electron moves to a higher level. Energy: hf = Ef - Ei By combining the idea of energy levels with classical theory, Bohr was able to predict the radius of the hydrogen atom.

Balmer Total energy of Hydrogen atom for level n. Negative because outside energy to raise n level. When an electron moves from an initial state ni to a final state nf, energy involved is: Balmer’s Equation:

Energy Levels We can now visualize the hydrogen atom with an electron at many possible energy levels. The energy of the atom increases on absorption (nf > ni) and de-creases on emission (nf < ni). Emission Absorption Energy of nth level: The change in energy of the atom can be given in terms of initial ni and final nf levels:

Spectral Series for an Atom The Lyman series is for transitions to n = 1 level. The Balmer series is for transitions to n = 2 level. n =2 n =6 n =1 n =3 n =4 n =5 The Pashen series is for transitions to n = 3 level. The Brackett series is for transitions to n = 4 level.

Change in energy of the atom. Example 3: What is the energy of an emitted photon if an electron drops from the n = 3 level to the n = 1 level for the hydrogen atom? Change in energy of the atom. DE = -12.1 eV The energy of the atom decreases by 12.1 eV as a photon of that energy is emitted. You should show that 13.6 eV is required to move an electron from n = 1 to n = .

Now on to quantum numbers…

Quantum Numbers PRINCIPAL: n energy level, the distance the orbital is from the nucleus (1, 2, 3, 4…) ANGULAR MOMENTUM: l shape (s = 0, p = 1, d = 2, f = 3) MAGNETIC: ml spatial orientation (0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.) SPIN: ms spin (+1/2 or -1/2)

Review Atomic number = # electrons Electrons occupy orbitals defined by n, l, m Each orbital can hold two electrons Orbitals  diffuse electron cloud “lower energy electron”  closer to nucleus Outer electrons: “valence” most reactive

Quantum Numbers The principal quantum number has the symbol n. n = 1, 2, 3, 4, ...... “shells” (n = K, L, M, N, ......) The electron’s energy depends principally on n. 1 2 3

Quantum Numbers The angular momentum quantum number has the symbol .  = s, p, d, f, g, h, .......(n-1)  tells us the shape of the orbitals. These orbitals are the volume around the atom that the electrons occupy 90-95% of the time.

Quantum Numbers The symbol for the magnetic quantum number is m, representing the spatial orientation. m = -  , (-  + 1), (-  +2), .....0, ......., ( -2), ( -1),  If  = 0 (or an s orbital), then m = 0. If  = 1 (or a p orbital), then m = -1,0,+1. y z x

Spin quantum number The last quantum number is the spin quantum number which has the symbol ms. The spin quantum number only has two possible values. ms = +1/2 or -1/2

Spin of electron

Spin quantum number effects: Every orbital can hold up to two electrons. Consequence of the Pauli Exclusion Principle. The two electrons are designated as having one spin up  and one spin down Spin describes the direction of the electron’s magnetic fields.

Re-Cap: Quantum Numbers PRINCIPAL: n energy level, distance from nucleus (1, 2, 3, 4…) ANGULAR MOMENTUM: l shape (s = 0, p = 1, d = 2, f = 3) MAGNETIC: ml spatial orientation (0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.) SPIN: ms spin (+1/2 or -1/2)

Atomic Orbitals: s, p, d, f Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest. s orbital properties: There is one s orbital per n level.  = 0 and only one value of m = 0

The only thing that changes for s orbitals is n. s orbitals are spherically symmetric For every s orbital: = 0 and ml = 0 The only thing that changes for s orbitals is n.

1s orbital of hydrogen Distance from nucleus

Probability densities for finding an electron at a given radius 1s, 2s, and 3s orbitals for hydrogen

Three dimensional depictions of electron distribution

p orbitals p orbital properties: The first p orbitals appear in the n = 2 shell. p orbitals are peanut, dumbbell or butterfly shaped volumes. There are 3 p orbitals per n level. The three orbitals are named px, py, pz.  = 1 for all p orbitals. m = -1,0,+1 (designate the three orientations)

p orbitals are peanut or dumbbell shaped.

p orbitals are peanut or dumbbell shaped.

2p orbital

d orbital properties: The five d orbitals have two different shapes: The first d orbitals appear in the n = 3 shell. The five d orbitals have two different shapes: 4 are clover leaf shaped. 1 is peanut shaped with a doughnut around it. The orbitals lie directly on the Cartesian axes or are rotated 45o from the axes. There are 5 d orbitals per n level. The five orbitals are named: They have an  = 2. m = -2,-1,0,+1,+2 (5 values of m )

 = 2 m = -2,-1,0,+1,+2

 = 2 m = -2,-1,0,+1,+2 d orbital shapes

f orbital properties: The f orbitals have the most complex shapes. The first f orbitals appear in the n = 4 shell. The f orbitals have the most complex shapes. There are seven f orbitals per n level. The f orbitals have complicated names. They have an  = 3 m = -3,-2,-1,0,+1,+2, +3 7 values

 = 3 m = -3,-2,-1,0,+1,+2, +3 7 values

f orbital shapes