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Quantum Mechanical AtomPart I:Electromagnetic RadiationChapter 8 Section 1 & 2of Jespersen 6th ed)

Dr. C. Yau

Spring 2013

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Electromagnetic Radiation

Electromagnetic radiation carries E thru space by means of a wave.

Properties of a wave: (Refer to lec. Notes)

•Wavelength (, pronounced lambda)

•Frequency (, pronounced nu)

•Amplitude (A)

•Energy of the photon (uniform packets of E, proportional to frequency)

Units of Measurement

Wavelength: m, cm, m, nm,

angstrom = Å

1 nm = 10 Å

1 m = 1010 Å

Frequency: cycles per second = 1/sec = sec-1

1 Hertz = = 1 Hz =1 sec-1

Energy: J, kJ, ergs

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How are they related?

x = c = 2.998x108 m s-1 (speed of light)

is inversely proportional to

Example 8.1 p. 253

Mycobacterium tuberculosis, the organism that causes tuberculosis, can be completely destroyed by irradiation with UV light with a wavelength of 254 nm. What is the frequency of this radiation?

Example 8.2 p. 308

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Radio station WKXR is an AM radio station broadcasting from Asheboro, N Carolina, at a frequency of 1260 kHz. What is the wavelength of these radio waves expressed in meters?

Do Pract Exer 1, 2, 3 p.308

Energy of a Light Wave

The energy carried by a light wave is said to be in “discrete” packets called "photons."

Size of energy of the photons is proportional to the frequency of the wave.

E = h where h = Planck's constant

= 6.626x10-34 J s

You don’t need to memorize constants.

Relationship between wavelength, frequency & energy of the photon

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The “Rainbow”

• The rainbow is a small region of the electromagnetic radiation spectrum, the “visible” region of the spectrum.

• You should know the names of the rest of the regions of the spectrum, and in order of energy, frequency and wavelength. (See lecture notes.)

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Electromagnetic Radiation Spectrum

Fig. 8.3 p. 310 9

10Absorption of light by chlorophyll

What is the energy of a photon of the red light at 700. nm?

• What do we know about energy and the wave?

• How is wavelength related to frequency?

• How is energy related to wavelength?

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Continuous vs. Line Spectrum

What do we see if ordinary white light is passed through a prism?

If we pass a current through a partially evacuated tube of a gas, a light is emitted.

If this emitted light is passed through a prism, we do not see a continuous rainbow, instead we see...

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Figure 8.7 p. 314 Emission Line Spectrum13

We see discrete colored lines on a black background

Line Spectra are like fingerprints

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Line Spectrum of H2

A mathematician came up with an equation that describes the pattern of lines observed for hydrogen (the Rydberg Eqn).

The equation does not EXPLAIN why there is such a pattern.

Bohr came up with his Planetary Model of the Atom that EXPLAINS why hydrogen would produce such a pattern of lines.

(See lecture notes.)15

Bohr's CalculationsEach emission line of hydrogen is due to the

energy released in the transition of an electron from a higher E level to a lower one.

Bohr's equation En = B/n2

Bohr's constant, B = 2.180x10-18 J

This allows us to calculate the E of each level.

The amount of E released is equal to ΔE.

ΔE = Ehi – Elo

Once we have calculated ΔE, we can determine the corresponding and .

(See lecture notes.)

Why Schroedinger has to come up with a different model:

Bohr’s theory could predict emission lines for one electron system ONLY.

What are one-electron systems?

How is Schroedinger’s model different from Bohr’s?

See next PowerPoint.

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