Waves &

Bohr’s TheoryChapter 7 §1-4

Waves

Wavelength, λ, in meters (m)The length of a wave from crest to crest or trough to

trough.

Frequency, υ, in inverse seconds (s-1)The number of waves that pass in a given amount

of time.

Light’s Wave Characteristics

Light’s Wave Characteristics

Speed of light equation

c c = speed of light, 3.00x108 m/sλ = wavelength, in mν = frequency, in Hz or s–1

Light’s Wave Characteristics

What is the frequency of red light having a wavelength of 681 nm?681 nm = 6.81x10–7 m3.0x108 m/s = (6.81x10–7 m)(υ)υ = 4.41x1014 s–1

Max Planck

Quantized

Planck’s Equation

n = integer other than zero, no unit, represents the energy level of the atomh = Planck’s constant, 6.63x10–34 J•sν = frequency, in Hz or s–1

E = energy of a quantum – amount of energy to move an e– from its present energy to its next higher one

E nh

The Photoelectric Effect

Although the photoelectric effect was first discovered by Heinrich Hertz in 1887, Albert Einstein incorporated Planck’s ideas into the explanation of the photoelectric effect.

The Photoelectric Effect

Einstein stated that electrons could move within their atoms if a minimum amount of energy were reached.

Let’s Practice

The blue-green line of the hydrogen atom spectrum has a wavelength of 486 nm. What is the energy of a photon of this light? 486 nm = 4.86x10–7 m

3.0x108 m/s = (4.86x10–7 m) (υ)υ = 6.17x1014 s–1

E = (1)(6.63x10–34 J•s)(6.17x1014 s–1)E = 4.09x10–19 J

Bohr’s Line Spectra

Bohr noticed that elements emitted a line spectrum.

Bohr’s Line Spectra

He hypothesized that each line in the spectra were created when an electron fell from a higher energy level to a lower one within the atom.

Bohr’s Line Spectra

Here, the electron of the hydrogen atom is shown moving between the various energy levels.

Bohr’s Postulates

Bohr felt the need to explain two main issues: 1st – If electrons are negative

and protons are positive…..

Bohr’s Postulates

Bohr felt the need to explain two main issues: 2nd – How are the line spectra

being created?

Bohr’s Postulates

Postulate #1:Electrons only have specific

energy values and energy levels.

= the energy of a particular e– energy level

= the Rydberg constant = 2.18x10–18 J = integral value representing the

energy level (principal quantum number

2HREn

Bohr’s Postulates

Postulate #2:Electrons become excited by

collisions of atoms or absorption of energy – think of anything colored… it absorbs light to later emit (reflect) other colors

Electrons can change energy only by going from one energy level to another – making a transition.

Bohr’s Postulates

Postulate #2:The electron

absorbing energy

Bohr’s Postulates

Postulate #2:When an electron falls from a

higher energy level to a lower energy level, it emits a photon of light.

Bohr’s Postulates

Postulate #2: This energy of this photon

can be found by:

2 2f i

H Hn n

f i

R RE E E

n n

Bohr’s Postulates

Postulate #2: Remember that the energy of

a photon can be determined by:

2 2f i

H Hn n

f i

R RE E E

n n   h

Bohr’s Postulates

Postulate #2: Which can be related to

wavelength:

2 2f i

H Hn n

f i

R RE E E

n n   h   

ch

Bohr’s Postulates

Postulate #2:Which leads to the Balmer

equation:

This equation can calculate the wavelength of any electron falling to the 2nd energy level – emitting visible light.

7 12 2

1 1 11.097 10

2 i

x mn

Bohr’s Postulates

Postulate #2:By the end of Experiment

#13, you should be able to identify the Balmer Series, along with the Paschen Series and the Lyman Series.

Let’s Practice

What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes a transition from energy level n = 6 to level n = 3?

Let’s Practice

What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes a transition from energy level n = 6 to level n = 3?

∆E = E3 – E6 =

υ = 2.74x1014 s–1

c = λυ → 3.0x108 m/s = λ (2.74x1014 s–1)

λ = 1.09x10–6 m = 1090 nm (Infrared)

18 1819

2 2

2.18 10 2.18 101.82 10

3 6

J Jx J

19 341.82 10 6.636 10x J x J s