Bohr’s Model of the Atom • 1913

Science is not a one-man showThe work of other scientists help

lay a foundation for new discoveries

Bohr set out to explain

• The relationship between

- the emission lines observed in excited element’s spectrum and

- the element’s atomic structure

Red, green, blue and violet spectral lines

Classically, light is thought to be a wave• Light or electromagnetic

radiation is a wave in which

- electric field oscillates perpendicular to magnetic field through space

Wavelength (symbol: , called lambda)

= distance between any 2 adjacent identical points of a wave (i.e. between 2 crests or 2 troughs)

Frequency of a wave = # of wavelengths of that wave passing a fixed point in one second

Frequency symbol: , called nu or new Unit: 1/second or Hertz (Hz)

The shorter the wavelength, the higher the frequencyThe longer the wavelength, the lower the frequency

Math. relationship b/t wavelength and frequency

where c = 3.00 x 108 m/s = speed of light in a

vacuum

c = x

Or

c is fixed:

• If increases, will decrease

• If decreases, will increase

Rethinking light: Light also behave as a particle1. Blackbody radiation Widely accepted: - A heated object emits

light- The hotter it gets, higher

energy re-radiated e.g. UV, X-ray, Gamma rays but no object does this

E photon =h

- Planck proposed: light is not continuous as previously thought but discrete bundles of energy, called quanta

h = Planck’s constant = 6.626×10 −34 J s)⋅

Rethinking light: Light also behave as a particle

2. The photoelectric effect:

• Certain frequencies of light were able to knock electrons off the surface of metals

• Other frequencies regardless of the intensity of light, were unable to do so.

Bohr’s simple assumption

By now Bohr has inherited the ideas that- Light is quantized- Spectroscopy is a powerful tool to infer about

atomic structure

- Adding his own assumption: What if some aspects of atomic structure, such as electron orbits and energies, could only take on certain values?

What is spectroscopy?

• Analysis of the way matter absorbs or releases radiation

• Spectroscopy is used to:a) identify elements or compoundsAtomic Spectra: Fingerprints of Elements

Spectroscopy is used to:• b) obtain information about bonding and

structures of compounds

IR spectrum

Spectroscopy is used to:• c) Quantitatively determine the concentrations

of substances present.

A simple spectroscope

Two main types of atomic spectra:Emission vs. Absorption Spectra

“Bright-line Spectra” is atomic emission spectra in the visible range.

Absorption vs. Emission Spectra of Hydrogen

Note that the spectral lines are on the same wavelength.

Emission spectrum:As excited electrons relax to lower energy levels, light is emitted. This release of energy explains for the color lines on the emission spectrum of hydrogen atom.Many more lines but they’re in IR and UV regions and thus are not visible.

Absorption spectrum:Observed when we see white light passing through a glass tube containing Hydrogen gas. The Hydrogen atom absorb very specific wavelength of radiation resulting in missing lines in the continuous spectrum.

Advantages/Uses of Spectroscopy• a) can definitively distinguish between substances

with very similar physical and chemical properties.

eg. Members of the alkali metals family

K Na

Advantages/Uses of Spectroscopy• b) Sample is distant • Eg. Applications in Astronomy

Astronomers have made the first direct detection and chemical analysis of an atmosphere of a planet that exists outside our solar system.

Spectrum of the hot gases in a nearby star-forming region, the Omega Nebula (M17)

Advantages/Uses of Spectroscopy• b) Sample quantity is limited • eg. in Forensics “Crystal meth”

Back to Bohr’s model

Emission spectrum of heated hydrogen gas

• Bohr’s postulate #1:An electron can only sit in specific energy levels.

Energy levels of the e- in the H atom can be calculated as (R = Rydberg constant expressed in J = 2.18 x 10-18 J)

n = Principal Quantum number;

- Can only be integer 1, 2, 3…∞- indicates the orbit.

Energy also in J

A note about units of energy

• Joule is too big of a unit when dealing with e-• New energy unit: The electron-volt (eV) • Define: • 1eV ≈ 1.6 x10-19 J= the kinetic energy gained by an electron when accelerated through 1 volt of potential difference

Can also be expressed as

When n =1, lowest possible energy or ground state energy of a hydrogen electron = -13.6 eV

Where E expressed in J Where E expressed in eV

Why the negative sign?

Because:- the energy of an electron in orbit is compared with the energy of an electron that is free from its nucleus (n=∞) This free e- has an energy = 0

- e- in orbit is more stable than e- infinitely far from nucleus, the energy of an electron in orbit is always negative.

Where E expressed in J

Where E expressed in eV

Energy level in Hydrogen atom

How to get this value?

Note that because of the negative sign, E1 is the lowest in energy (instead of the highest)

• Absorption of Energy = Excitation

The quantum leap

If the incoming energy is exactly equal to the difference in energy between two orbits, the electron leaps to excited state

If the incoming energy is a little less or greater, it passes through the atom unaffected

When moving within these allowed energy states (stationary states) the electron does NOT emit (release) energy.

• Emission of Energy = Relaxation

The quantum leap

• As excited e- relaxes to lower energy level, it releases the energy difference between the two orbits in the form of electromagnetic radiation.

• This explains spectral lines of excited atoms and the origin of light itself.

Energy of emitted photon = h = Efinal - Einitial

Bohr’s postulate #2: Electron transitions

Excitation RelaxationElectron moves to

higher E level

lower E level

Energy is

Absorbed Released

Form of Energy

Heat, light, electrical

Electro-magnetic radiation

Relaxation from higher orbit to

Energy emitted Name of the series

n=1 UV Lymann=2 Visible Balmern=3 IR Paschenn=4 IR Brackett

What happens to a sample of hydrogen gas (in a discharge tube) when an electric current is run through

it?

• Electrical energy is absorbed and excites the electrons

• Relaxation follows

• H2 emits a purplish light is emitted.

• Color light perceived by the eyes

https://youtu.be/955snB6HLB4

Emission in real life

• Flame test helps identify the metals

• Fireworks• LED light vs sodium vapor

street lamps

Emission in real life

Coop. Learning

When E= -13.6/ n2 in eV In Joules1eV = 1.6 x10-19 J

n=1 n=2

n=3

n=4

n=5

n=6

n= infinity

When E= -13.6/ n2 in eV

In Joules1eV = 1.6 x10-19 J

n=1

E = -13.6 eV E= -13.6 x 1.6x 10-19 = 2.176x 10-18J

n=2 E= -13.6/4 eV E= -5.44 x 10-19 J

n=3 E= - 1.51 eV E= -2.42 x 10-19 J

n=4 E= -0.85 eV E= -1.36 x 10-19 J

n=5 E= -0.54 eV E= -8.70 x 10-20 J

n=6 E= -0.38 eV E= -6.04 x 10-20 J

n= infinity E= 0 E= 0 J