IB Chemistry on Line Emission Spectrum, Bohr Model and Electromagnetic Spectrum

Electromagnetic Spectrum

Electromagnetic spectrum ranges from Radiowaves to Gamma waves. - Form of energy - Shorter wavelength -> Higher frequency -> Higher energy - Longer wavelength -> Lower frequency -> Lower energy

Electromagnetic radiation • Travel at speed of light, c = fλ -> 3.0 x 108 m/s • Light Particle – photon have energy given by -> E = hf • Energy photon - proportional to frequency

Inverse relationship between- λ and f Wavelength, λ - long

Frequency, f - low

Wavelength, λ - short Frequency, f - high

Plank constant • proportionality constant bet energy and freq

Excellent video wave propagation Click here to view.

Electromagnetic Wave propagation.

Wave

Electromagnetic radiation

Electromagnetic radiation • Moving charges/particles through space • Oscillating wave like property of electric and magnetic field • Electric and magnetic field oscillate perpendicular to each other and perpendicular to direction of wave propagation.

Electromagnetic wave propagation

Wave – wavelength and frequency - travel at speed of light

Violet

λ = 410nm

Red

f = c/λ = 3 x 108/410 x 10-9

= 7.31 x 1014 Hz

E = hf = 6.626 x 10-34 x 7.31 x 1014

= 4.84 x 10-19 J

λ = 700nm

f = c/λ = 3 x 108/700 x 10-9

= 4.28 x 1014 Hz

E = hf = 6.626 x 10-34 x 4.28 x 1014

= 2.83 x 10-19 J

Click here to view video

Electromagnetic Wave propagation.

Wave

Electromagnetic radiation

Simulation on Electromagnetic Propagation

Click here to view simulation Click here to view simulation Click here to view simulation

Electromagnetic radiation • Moving charges/particles through space • Oscillating wave like property of electric and magnetic field • Electric and magnetic field oscillate perpendicular to each other and perpendicular to direction of wave propagation.

Click to view video -Wave-particle duality

Is it a particle or Wave?

Wave – wavelength and frequency - travel at speed of light

Electromagnetic Wave

Violet

λ = 410nm

Red

f = c/λ = 3 x 108/410 x 10-9

= 7.31 x 1014 Hz

λ = 700nm

f = c/λ = 3 x 108/700 x 10-9

= 4.28 x 1014 Hz

Which wave have higher frequency, if both have same speed reaching Y same time?

Violet

Y

Red

X

Wavelength – Distance bet two point with same phase, bet crest/troughs – unit nm Frequency – Number of cycle/repeat per unit time (cycles in 1 second) – unit Hz

Click here on excellent video red /violet wave

Light travel same speed Red flippers – long λ - less frequent Violet shoes – short λ - more frequent

Click here to view video energy photon

http://www.astrophys-assist.com/educate/orion/orion02.htm

Continuous Spectrum : Light spectrum with all wavelength/frequency

Emission Line Spectrum : • Spectrum with discrete wavelength/ frequency • Emitted when excited electrons drop from higher to lower energy level

Absorption Line Spectrum : • Spectrum with discrete wavelength/frequency • Absorbed when ground state electrons are excited

Atomic Emission Vs Atomic Absorption Spectroscopy

Ground state

Excited state Electrons from excited state

Emit radiation when drop to ground state

Radiation emitted

Emission Spectrum

Electrons from ground state

Absorb radiation to excited state

Electrons in excited state

Radiation absorbed

Continuous Spectrum Vs Line Spectrum

Line Emission Spectra for Hydrogen

Energy supplied to atoms • Electrons excited - ground to excited states • Electrons exist fixed energy level (quantum) • Electrons transition from higher to lower, emit energy of particular wavelength/frequency - photon • Higher the energy level, smaller the difference in energy bet successive energy level. • Spectrum converge (get closer) with increase freq. • Lines spectrum converge- energy levels also converge • Ionisation energy determined (Limit of convergence)

N = 3-2, 656nm

N= 4-2 486nm

N= 5-2 434nm

N= 6-2 410nm

Visible region- Balmer Series

UV region

Lyman Series n=∞ → n= 1

Visible region Balmer Series n=∞ → n= 2

IR region Paschen Series n=∞ → n= 3

Line Emission Spectra • Energy supplied • Electrons surround nucleus in allowed energy states (quantum) • Excited electron return to lower energy level, photon with discrete energy/wavelength (colour) given out. • Light pass through spectroscope (prism/diffraction grating) to separate out diff colours

Click here to view video Click here to view video

Videos on line emission

Line Emission Spectroscopy

Ground state

Excited state

Hydrogen Emission Spectroscopy – Visible region (Balmer Series)

Line Emission Spectra for Hydrogen

Visible region Balmer Series n=∞ → n= 2

Hydrogen discharge tube Hydrogen Emission Spectroscopy

n = 3-2 n= 4-2 n= 5-2

λ = 656nm

f = c/λ = 3 x 108/656 x 10-9

= 4.57 x 1014 Hz

E = hf = 6.62 x 10-34 x 4.57 x 1014

= 3.03 x 10-19 J

λ = 434nm λ = 486nm

f = c/λ = 3 x 108/434 x 10-9

= 6.90 x 1014 Hz

E = hf = 6.62 x 10-34 x 6.90 x 1014

= 4.56 x 10-19 J

More energetic violet line Less energetic red line

2

1

3

4 5

Click here for detail notes Click here video line emission spectrum

Bohr Model for Hydrogen Atom – Ionization Energy

Niels Bohr Model (1913) • Electrons orbit nucleus. • Orbits with discrete energy levels – Quantized. • Transition electron bet diff levels by absorb/emit radiation with frequency, f determined by energy diff bet levels -ΔE = hf • Energy light emit/absorb equal to diff bet energy levels

Electronic Transition bet levels Energy level Bohr Model

1

2

3

4 5 ∞

Light emitted equal to difference bet energy levels, -ΔE = hf

Plank equation

Ionisation energy determined (Limit of convergence)

Line spectrum converge (get closer) with increase freq

Higher energy level n, smaller the difference in energy bet successive energy level.

Lines in spectrum converge- energy levels also converge

Visible region Balmer Series n=∞ → n= 2

Increase freq

UV region Lyman Series n=∞ → n= 1

ΔE = hf

Light energy - ΔE = hf Frequency = ΔE/h

Increase freq

Line spectrum converge (get closer) with increase freq

Ionization energy Transition electron from 1 ->∞

line converge line converge

Light given off

Energy Level/Ionization Energy Calculation

1

2

3

4

5 ∞

Formula - energy level, n (eV) Energy difference bet level 3 to 2

1

2

n = energy level

Lower energy level, n - more stable electron - more – ve (-13.6eV) - Less energetic

Higher energy level, n - more unstable electron - More + ve ( less negative) - More energetic

Energy level, n= 1 = -13.6/n2

= -13.6/1 = -13.6 eV

Energy level, n= 2 = -13.6/n2

= -13.6/22

= -3.4 eV

Energy level, n= 3 = -13.6/n2

= -13.6/32

= -1.51 eV

3

4

5

Energy difference, n= 3-2

= -1.51 – (-3.4) eV = 1.89 eV = 1.89 x 1.6 x 10-19 J = 3.024 x 10-19 J

1eV – 1.6 x 10-19 J h = 6.626 x 10-34 Js

Light energy - ΔE = hf Frequency, f = ΔE/h

Frequency, f = ΔE/h f = 3.024 x 10-19 /6.626 x 10-34

= 4.56 x 1015 Hz

λ = c/f = 3 x 108/4.56 x 1015

= 657 x 10-9

= 657nm

Ionization energy Transition electron from 1 ->∞

constant

Light given off

Light given off

1

2

3

4

5

6

1

2

3

4

Ionization Energy for Hydrogen Atom

1

2

3

4

5 ∞

Ionization energy Min energy to remove 1 mole electron from 1 mole of element in gaseous state M(g) M+ (g) + e

Energy difference bet level 3 to 2

1

2

n = energy level

Energy level, n= 1 = -13.6/n2

= -13.6/1 = -13.6 eV

3

4

5

Energy difference, n= 3-2

= -1.51 – (-3.4) eV = 1.89 eV = 1.89 x 1.6 x 10-19 J = 3.024 x 10-19 J

Light energy - ΔE = hf Frequency, f = ΔE/h

Frequency, f = ΔE/h f = 3.024 x 10-19 /6.626 x 10-34

= 4.56 x 1015 Hz

λ = c/f = 3 x 108/4.56 x 1015

= 657 x 10-9

= 657nm

Ionization energy Transition electron from 1 ->∞

Energy level, n= ∞ = -13.6/n2

= -13.6/∞ = o eV

∞

Energy Absorb

Energy difference, n= 1-> ∞

= 0 – (-13.6) eV = 13.6 eV = 13.6 x 1.6 x 10-19 J = 2.176 x 10-18 J for 1 electron

Energy absorb for 1 MOLE electron - 2.176 x 10-18 J - 1 electron - 2.176 x 10-18 x 6.02 x 1023 J - 1 mole - 1309kJ mol-1

Light given off, electronic transition from high -> low level

Energy Released

Light/photon ABSORB by electron

Light given off

Light given off

Light given off

electron

1

2

3

4

5

6

1

2

3

4

5

Energy/Wavelength – Plank/Rydberg Equation

ΔE = hf

1

2

3

4

5 ∞

Formula – Plank Equation Electron transition from 3 -> 2

1

2

n = energy level

R = Rydberg constant R = 1.097 x 107 m-1

3

4

5

Rydberg Equation to find wavelength

nf = 2, ni = 3 R = 1.097 x 107

λ = 657 x 10-9

= 657 nm

Nf = final n level Ni = initial n level

f = c/λ = 3 x 108/657 x 10-9

= 4.57 x 1014 Hz

Energy photon- high -> low level

Click here to view video Click here to view video

Click here on energy calculation

∞

Energy Level/Ionization Energy Calculation

Light given off

Light given off

Rydberg Eqn find wavelength emit

1

2

3

4

5

1

2

3

4

5 ∞

Electron transition from 3 -> 2

1

2

n = energy level

3

4

5

nf = 2, ni = 3 R = 1.097 x 107

λ = 657 x 10-9

= 657 nm

f = c/λ = 3 x 108/657 x 10-9

= 4.57 x 1014 Hz

Energy photon- high -> low level

∞

Ionization Energy for Hydrogen Atom

Ionization energy Min energy to remove 1 mole electron from 1 mole of element in gaseous state M(g) M+ (g) + e

Ionization energy Transition electron from 1 -> ∞

Energy Absorb

Rydberg Eqn find ionization energy

nf = ∞, ni = 1 R = 1.097 x 107

λ = 9.11 x 10-8

Energy absorb for 1 MOLE electron - 2.179 x 10-18 J - 1 electron - 2.179 x 10-18 x 6.02 x 1023 J - 1 mole - 1312kJ mol-1

Energy, E = hf = 6.626 x 10-34 x 3.29 x 1015

= 2.179 x 10-18 J for 1 electron

f = c/λ = 3 x 108/9.11 x 10-8

= 3.29 x 1015 Hz

Light/photon ABSORB by electron

electron

Light given off, electronic transition from high -> low level

Light given off

Light given off

Rydberg Eqn find wavelength emit

1

1

3

4

5 6 7

1

2

3

4

5

1

2

3

4

5

∞

1

2

n = energy level

3

4

5

Energy = hv (1 mole) = 6.626 x 10-34 x 32.26 x 1014 x 6.o2 x 1023

= 1312KJ mol-1

∞

Light/photon ABSORB by electron

electron

6 6 7 7

8 8

Calculating Ionization Energy from Lyman Series ( n = 1 to ∞ )

Excited energy level

Frequency, v / x 1014 s-1

ΔV / x 1014 s-1

2 24.66 4.57

3 29.23 1.60

4 30.83 0.74

5 31.57 0.40

6 31.97 0.24

7 32.21 0.16

8 32.37

Line spectrum converge (get closer) with increase freq

Ionization energy determined from (Limit of convergence)

Ionization energy Transition electron from 1 ->∞

Ionization energy Transition electron from 1 ->∞

Difference bet freq successive lines

Find freq v, at which it converge Δv = 0

Δv = 0

Plot graph v against Δv

Find Ionization Energy 1

2

3

Linear curve fit equation Δv = -0.5897v + 19.022

4

Freq, v when Δv = 0 -0.5897v + 19.022 = 0 v = 19.022 x 1014 s-1

0.5897 v = 32.26 x 1014s-1

5

Question adapted from Pearson

1

2

3

4

5

∞

1

2

n = energy level

3

4

5

Energy = hv (1 mole) = 6.626 x 10-34 x 32.86 x 1014 x 6.o2 x 1023

= 1312KJ mol-1

Energy for n level: ∞

6 6 7 7

8 8

Calculating Ionization Energy from Lyman Series ( n = 1 to ∞ )

Excited energy level, n

Excited energy level, 1/n2

Frequency V / x 1014 s-1

2 0.25 24.66

3 0.11 29.23

4 0.0625 30.83

5 0.04 31.57

6 0.027 31.97

7 0.02 32.21

8 0.015 32.37

Find freq v, when 1/n2 = 0

Plot graph v against 1/n2

Find Ionization Energy 1

2

3

Linear curve fit equation v = -32.84 (1/n2) + 32.86

4

Freq, v when 1/n2 = 0 v = -32.84 (1/n2) + 32.86 v = 32.86 x 1014 s-1

5

Question adapted from Pearson

2

6.13

nE

hvE

2

6.13

nhv

2

6.13

hnv

cnh

v

2

16.13

Plot graph v against 1/n2

Continuous Spectrum Light spectrum with all wavelength/frequency

Emission Line Spectrum • Spectrum with discrete wavelength/ frequency • Excited electrons drop from higher to lower energy level

Continuous Spectrum Vs Line Spectrum

Click here spectrum for diff elements Click here spectrum for diff element Click here on quantum mechanic, structure of atom

Click here to view excellent simulation Click here to view simulation

Excellent simulation on emission spectrum

Emission line spectrum for different elements

Click here to view simulation

Video on quantum mechanics