Quantum Theory & Bohr’s Model of the Atom

Ch. 4 - Electrons in Atoms

A. Quantum Theory

Planck (1900)

Observed - emission of specific colors of light from hot objects

Concluded - energy is emitted in small, specific amounts (quanta)

Quantum - minimum amount of energy that can be lost or gained by an atom.

A. Quantum Theory

Planck (1900)

vs.

Classical Theory Quantum Theory

A. Quantum Theory

Einstein (1905)

Observed - photoelectric effect

A. Quantum Theory

Einstein (1905)

Concluded - light has properties of both waves and particles

“wave-particle duality”

Photon - particle of light that carries a quantum of energy

A. Quantum Theory

E: energy (J, joules)h: Planck’s constant (6.626 10-34 J/Hz): frequency (Hz)

E = h

The energy of a photon is proportional to its frequency of the light.

A. Examples

GIVEN:

E = ? = 4.57 1014 Hzh = 6.626 10-34 J/Hz

WORK:

E = h

E = (6.626 10-34 J/Hz)(4.57 1014 Hz)

E = 3.03 10-19 J

EX 1: Find the energy of a red photon with a frequency of 4.57 1014 Hz.

A. Examples

GIVEN:

E = ?= 1.0 10-9 m

c = 3.00 108 m/sh = 6.626 10-34 J/Hz

WORK:

E = h = hc/ λ = (6.626 ·10-34 J/Hz)(3.00 ·108 m/s)

1.0 x 10-9 m

E = 2.0 10-16 J

EX 2: Find the energy of a photon whose wavelength is 1.0 10-9 m.

B. Bohr’s Model

Linked photon emission with an atom’s electrons (e-)

In Bohr’s model, e- exist only in orbits with specific amounts of energy called energy levels

B. Bohr’s Model

Therefore…

e- can only gain or lose certain amounts of energy (quanta)

only certain photons are produced

each photon has a unique frequency, and therefore a unique color of light is seen

B. Bohr’s Model

ground state(low energy orbit; closer to nucleus)

excited state(high energy orbit;

further from nucleus)

ENERGY IN PHOTON OUT

ee--

electron

“relaxes”

Line Emission Spectrum produced

D. Bohr Model

1

23

456Energy of photon

depends on the difference in energy levels

Bohr’s calculated energies matched the IR (Paschen), visible (Balmer), and UV (Lyman) lines for the H atom

Hydrogen Emission Spectrum

D. Other Elements

Each element has a unique bright-line emission spectrum.

“Atomic Fingerprint”

Helium

Bohr’s calculations only worked for hydrogen!