2. Line spectrum – each line corresponds to a discrete wavelength:
Continuous spectrum (results when white light is passed through a prism) – contains all the wavelengths of visible light
Line spectrum – each line corresponds to a discrete wavelength:
Hydrogen emission spectrum
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3. Refraction of White Light
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4. The Line Spectrum of Hydrogen
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5. Significance
Only certain energies are allowed for the electron in the hydrogen atom.
Energy of the electron in the hydrogen atom is quantized.
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6. CONCEPT CHECK!
Why is it significant that the color emitted from the hydrogen emission spectrum is not white? How does the emission spectrum support the idea of quantized energy levels?
If the levels were not quantized, we’d probably see white light. This is because all possible value of energy could be released, meaning all possible colors would be emitted. All the colors combined make white light. Since only certain colors are observed, this means that only certain energy levels are allowed. An electron can exist at one level or another, and there are regions of zero probability in between.
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7. Ground state – lowest possible energy state (n = 1)
Electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.
Bohr’s model gave hydrogen atom energy levels consistent with the hydrogen emission spectrum.
Ground state – lowest possible energy state (n = 1)
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8. Electronic Transitions in the Bohr Model for the Hydrogen Atom a) An Energy-Level Diagram for Electronic Transitions
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9. Electronic Transitions in the Bohr Model for the Hydrogen Atom b) An Orbit-Transition Diagram, Which Accounts for the Experimental Spectrum
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10. For a single electron transition from one energy level to another:
ΔE = change in energy of the atom (energy of the emitted photon)
nfinal = integer; final distance from the nucleus
ninitial = integer; initial distance from the nucleus
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11. The model correctly fits the quantized energy levels of the hydrogen atom and postulates only certain allowed circular orbits for the electron.
As the electron becomes more tightly bound, its energy becomes more negative relative to the zero-energy reference state (free electron). As the electron is brought closer to the nucleus, energy is released from the system.
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12. Bohr’s model is incorrect. This model only works for hydrogen.
Electrons move around the nucleus in circular orbits.
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13. Which transition results in the longest wavelength of light?
EXERCISE!
What wavelength of light is emitted when an excited electron in the hydrogen atom falls from:
n = 5 to n = 2
n = 4 to n = 2
n = 3 to n = 2
Which transition results in the longest
wavelength of light?
For each transition, use ΔE = hc / λ = (–2.178×10–18)[(1/nf) – (1/ni)]. Solve for λ in each case.
a) blue (λ = 434 nm)
b) green (λ = 486 nm)
c) orange/red (λ = 657 nm)
The longest wavelength of light is from transition n = 3 to n = 2 (letter c).
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