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• Review of 5.1:
• All waves have distinct amplitudes, frequency, periods and wavelengths.
• All electromagnetic waves travel at the speed of light. C = (3.0x108 m/s)
• C = f• The relationship between the energy
and frequency is E = hf• All elements have their own individual
atomic emission spectrum and absorption spectrum.
Section 5-2
Section 5.2 Quantum Theory and the Atom
• Compare the Bohr and quantum mechanical models of the atom.
atom: the smallest particle of an element that retains all the properties of that element, is composed of electrons, protons, and neutrons.
• Explain the impact of de Broglie's wave article duality and the Heisenberg uncertainty principle on the current view of electrons in atoms.
• Identify the relationships among a hydrogen atom's energy levels, sublevels, and atomic orbitals.
Section 5-2
Section 5.2 Quantum Theory and the Atom (cont.)
ground state
quantum number
de Broglie equation
Heisenberg uncertainty principle
Wavelike properties of electrons help relate atomic emission spectra, energy states of atoms, and atomic orbitals.
quantum mechanical model of the atom
atomic orbital
principal quantum number
principal energy level
energy sublevel
Section 5-2
Bohr's Model of the Atom
• The dual wave-particle model of light could not explain all phenomena of light. In particular, it couldn’t explain why emission spectra was discontinuous.
• Niels Bohr, a Danish physicist that worked in Rutherford’s lab, proposed a model that would match hydrogen’s emission spectrum.
• In Bohr’s model, the atom has only certain allowable energy states. (circular orbits)
• The lowest allowable energy state of an atom is called its ground state.
• When an atom gains energy, it is in an excited state.
Section 5-2
Bohr's Model of the Atom (cont.)
• In Bohr’s model, atom’s with smaller energy states will have electrons in smaller orbits.
• Even Hydrogen can have many different excited states, depending on where its one electron is located.
Section 5-2
Bohr's Model of the Atom (cont.)
• Each orbit was given a number, n, called the quantum number.
Section 5-2
Bohr's Model of the Atom (cont.)
• Hydrogen’s single electron is in the n = 1 orbit in the ground state. No energy radiates in this state.
• When energy is added, the electron moves to the n = 2 orbit. This raises the electron to an excited state.
• If the electron would then drop from the higher orbit to a lower one, it will release energy in the form of a photon as it drops. The photon corresponds to the energy difference between the two levels.
• (p.148) • Because there are only certain energy
levels, there are only certain frequencies of radiation that can be emitted. E = hf
• Think of this like rungs of a ladder.• Just as you can only go up or down from
rung to rung, an electron can only move from one orbit to another.
• Unlike ladder rungs, however, the energy levels are not evenly spaced.
• Electrons that drop from higher-energy orbits down to the 2nd orbit make all hydrogen’s visible lines—the Balmer series.
• Electrons in Hydrogen that drop from higher levels to the 1st orbit release ultraviolet light and are in the Lyman series.
• Electrons in Hydrogen that drop from higher orbits to the 3rd orbit radiate infrared and are in the Paschen series.
Section 5-2
Bohr's Model of the Atom (cont.)
Section 5-2
Bohr's Model of the Atom (cont.)
Section 5-2
Bohr's Model of the Atom (cont.)
• Bohr’s model explained the hydrogen’s spectral lines, but failed to explain any other element’s lines.
• The behavior of electrons is still not fully understood, but it is known they do not move around the nucleus in circular orbits.
Section 5-2
The Quantum Mechanical Model of the Atom
• Mid 1920s, Frenchman Louis de Broglie (1892–1987) hypothesized that particles, including electrons, could also have wavelike behaviors.
• He compared light waves to waves made on musical instruments with fixed ends.
• On the instruments, only multiples of half wavelengths are possible.
• Similarly, de Broglie reasoned that only odd numbers of wavelengths are allowed in a circular orbit with a fixed radius.
Section 5-2
The Quantum Mechanical Model of the Atom (cont.)
• The figure illustrates that electrons orbit the nucleus only in whole-number wavelengths.
Section 5-2
The Quantum Mechanical Model of the Atom (cont.)
*de Broglie proposed that if waves can act like particles, the reverse must also be true.
The de Broglie equation predicts that all moving particles have wave characteristics.
represents wavelengthsh is Planck's constant.m represents mass of the particle. represents velocity .
• If all moving particles generate waves, why don’t we see them? Let’s look at a car moving at 25 m/s and having a mass of 910-kg. What wavelength of light will it have?
• German Werner Heisenberg (1901-1976), showed it is impossible to take any measurement of an object without disturbing it.
• Heisenberg compared trying to measure an electron’s position to trying to find a helium-filled balloon in a darkened room.
• The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time.
• The only quantity that can be known is the probability for an electron to occupy a certain region around the nucleus.
Section 5-2
The Quantum Mechanical Model of the Atom (cont.)• When a photon interacts with an electron at rest,
both the velocity and position of the electron are modified.
• The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time.
Section 5-2
The Quantum Mechanical Model of the Atom (cont.)
• 1926, Austrian Erwin Schrodinger (1887-1961) continued the wave- particle theory.
• Schrödinger treated electrons as waves in a model called the quantum mechanical model of the atom.
• Like Bohr’s model, this model limits an electron’s energy to certain values. It does not try to describe the electron’s path. His model is a very complex model using wave functions.
• Schrödinger’s equation applied equally well to elements other than hydrogen.
Section 5-2
The Quantum Mechanical Model of the Atom (cont.)• The wave function predicts a three-dimensional region around the nucleus called the atomic orbital.
• The density at a given point is proportional to the probability of finding an electron at that point.
Section 5-2
Hydrogen Atomic Orbitals
• Just as Bohr’s model had numbers assigned to electron orbits, so does the quantum mechanical model. There are 4 quantum numbers for orbitals.
• Principal quantum number (n) indicates the relative size and energy of atomic orbitals.
• n specifies the atom’s major energy levels, called the principal energy levels. As n increases, the orbital is larger and the atom’s energy increases. The lowest principle energy level has a principal quantum number of 1.
• A hydrogen atom in ground state will have a single electron in the n = 1 orbital.
Section 5-2
Hydrogen Atomic Orbitals (cont.)
• Energy sublevels are contained within the principal energy levels.
• The numbers of sublevels in a principal energy level increase as n increase, much like there are more seats per row as you go higher up in a stadium.
• Shapes of orbitals:– All s orbitals are spherical– All p orbitals are dumbbell-shaped– d and f orbitals do not all have the same
shape.– Orbitals in higher sublevels are bigger than
ones in lower sublevels. – (2s is bigger than 1s)
Section 5-2
Hydrogen Atomic Orbitals (cont.)
• Each energy sublevel relates to orbitals of different shape.
Section 5-2
Hydrogen Atomic Orbitals (cont.)
• The number of orbitals related to each sublevel is always an odd number.
• The maximum number of orbitals for each principal energy level equals n2.
2
A. A
B. B
C. C
D. D
Section 5-2
A B C D
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Section 5.2 Assessment
Which atomic suborbitals have a “dumbbell” shape?
A. s
B. f
C. p
D. d
A. A
B. B
C. C
D. D
Section 5-2
Section 5.2 Assessment
A B C D
0% 0%0%0%
Who proposed that particles could also exhibit wavelike behaviors?
A. Bohr
B. Einstein
C. Rutherford
D. de Broglie
