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© 2010 Pearson Education, Inc.
The Hydrogen Spectrum
Balmer’s formula
Wavelengths of visible lines in the hydrogen spectrum
Slide 29-13
© 2010 Pearson Education, Inc.
1. Schrödinger found that the energy of the hydrogen atom is given by the same expression found by Bohr, or
The integer n is called the principal quantum number.
2. The angular momentum L of the electron’s orbit must be one of the values
The integer l is called the orbital quantum number.
The Quantum-Mechanical Hydrogen Atom
Slide 29-22
© 2010 Pearson Education, Inc.
3. The plane of the electron’s orbit can be tilted, but only at certain discrete angles. Each allowed angle is characterized by a quantum number m, which must be one of the values
The integer m is called the magnetic quantum number because it becomes important when the atom is placed in a magnetic field.
3. The electron’s spin can point only up or down. These two orientations are described by the spin quantum number ms, which must be one of the values
The Quantum-Mechanical Hydrogen Atom
Slide 29-23
© 2010 Pearson Education, Inc.
Energy Levels in Multielectron AtomsHydrogen atom Multielectron atom
Slide 29-25
© 2010 Pearson Education, Inc.
Excited States and the Pauli Exclusion PrincipleHelium atom Lithium atom
Slide 29-26
© 2010 Pearson Education, Inc.
Reading Quiz1. What is the “Balmer formula” a formula for?
A. Masses of atomic nuclei of hydrogen isotopes
B. Wavelengths in the hydrogen emission spectrum
C. Energies of stationary states of hydrogen
D. Probabilities of electron position in stationary states of hydrogen
Slide 29-6
© 2010 Pearson Education, Inc.
Answer 1. What is the “Balmer formula” a formula for?
A. Masses of atomic nuclei of hydrogen isotopes
B. Wavelengths in the hydrogen emission spectrum
C. Energies of stationary states of hydrogen
D. Probabilities of electron position in stationary states of hydrogen
Slide 29-7
© 2010 Pearson Education, Inc.
Reading Quiz2. Which of the following aspects of the stationary states of
hydrogen does Bohr’s analysis of the hydrogen atom get right?
A. The existence of a “spin” quantum number
B. The existence of a “magnetic” quantum number
C. The shapes of the electron clouds
D. The energies of the stationary states
Slide 29-8
© 2010 Pearson Education, Inc.
Answer 2. Which of the following aspects of the stationary states of
hydrogen does Bohr’s analysis of the hydrogen atom get right?
A. The existence of a “spin” quantum number
B. The existence of a “magnetic” quantum number
C. The shapes of the electron clouds
D. The energies of the stationary states
Slide 29-9
© 2010 Pearson Education, Inc.
Checking UnderstandingSuppose that an atomic excited state decays to the ground state by emission of two photons, with energies E1 and E2. Is it possible for that excited state to decay to the ground state by emission of a single photon with energy E1 + E2?
A. It is always possible, for every atom.
B. It is never possible, for any atom.
C. It is always possible for hydrogen atoms, but is unlikely for other atoms.
Slide 29-31
© 2010 Pearson Education, Inc.
Answer Suppose that an atomic excited state decays to the ground state by emission of two photons, with energies E1 and E2. Is it possible for that excited state to decay to the ground state by emission of a single photon with energy E1 + E2?
A. It is always possible, for every atom.
B. It is never possible, for any atom.
C. It is always possible for hydrogen atoms, but is unlikely for other atoms.
Slide 29-32
© 2010 Pearson Education, Inc.
Checking UnderstandingWhich of the following is not a possible fluorescence process?
A. Absorption of red light and emission of green light
B. Absorption of ultraviolet light and emission of infrared light
C. Absorption of ultraviolet light and emission of green light
D. Absorption of blue light and emission of red light
Slide 29-35
© 2010 Pearson Education, Inc.
Answer Which of the following is not a possible fluorescence process?
A. Absorption of red light and emission of green light
B. Absorption of ultraviolet light and emission of infrared light
C. Absorption of ultraviolet light and emission of green light
D. Absorption of blue light and emission of red light
Slide 29-36