6.1.2 Energy Levels

Photons in / Photons out

Ionization

IONIZATION ENERGIES

Energy needed to liberate

electron from that level.

GROUND STATE Lowest possible

energy state for an electron in an

atom.

• A photon strikes an electron in the ground state of a hydrogen atom, liberating the electron.– What minimum energy did this photon have?

Example #1

13.6 eV

• A photon strikes an electron in the ground state of a hydrogen atom, liberating the electron.– What is the frequency of the photon that could

provide this energy?

Example #1

2.176 x 10-18 J

eVJx

eVxJ

1106.1

6.13

19

• A photon strikes an electron in the ground state of a hydrogen atom, liberating the electron.– What is the frequency of the photon that could

provide this energy?

Example #1

Ephoton = hf

2.176 x 10-18 J = (6.63 x 10-34 J·s) f

f = 3.3 x 1015 Hz

• What happens to an electron in the n = 2 state of a hydrogen atom if it is hit by a 5.4 electron-volt photon?

Example #2

The electron will leave the atom with a kinetic energy of 2.0 eV.

Level Jumps

• An electron will jump to a higher level if the ABSORBED photon has exactly the right energy.

• When an electron drops to a lower level a photon is EMITTED

fiphoton EEE

Equation

• What energy is needed to move an electron from the ground state of a hydrogen atom to its n = 4 level?

Example #3

Ephoton = Ei – Ef

Ephoton = -13.6 eV – -0.85 eV

Ephoton = -12.75 eV

• An electron drops from the n = 4 level to the n = 3 level of a hydrogen atom.– What is the energy of the emitted photon?

Example #4

Ephoton = Ei – Ef

Ephoton = -0.85 eV – -1.51 eV

Ephoton = +0.66 eV

• An electron drops from the n = 4 level to the n = 3 level of a hydrogen atom.– What is the frequency of this photon?

Example #4

Ephoton = hf

1.056 x 10-19 J = (6.63 x 10-34 J·s) f

f =1.6 x 1014 Hz

• When electrons drop from one energy level to another they can follow any path to the lower state. Each downward step produces a photon with a different energy.– How many different photons could be produced in a transition

from the n = 4 level of hydrogen to the n = 1 level?

– How many different photons could be produced in a transition from the d-level to the b-level of a mercury atom?

Example #5

6 possible photons

d

c

b 3 possible photons

n =4

n = 3

n = 2

n = 1

Absorption/Emission Spectrum• An EMISSION SPECTRUM is a pattern of bright lines on a

dark background.– Analyze glow of a heated sample

• An ABSORPTION SPECTRUM is a pattern of dark bands on a continuous spectrum.– Pass white light through a cold sample.

Absorption/Emission Spectrum• The existence of spectrums demonstrates that:

– Energy in atoms is QUANATIZED – comes in discrete jumps.

– Atoms can produce only specific sets of PHOTONS.

End of 6.1.2