Supplemental problems chapter 7
Electrons and light
Chem 201A
Dr. Baxley
Page 1 of 3
1. The wavelength of a diagnostic X-ray is 0.0120 nm. What is the frequency of these X-rays?
2. One common frequency band for US mobile phones (GSM) is 1.80×103 MHz. Calculate the wavelength (in
m and μm) of the EM radiation blasting out of your pocket.
3. The blue color of the sky results from the scattering of sunlight by air molecules. The blue light has a
frequency of 7.05×10 14 Hz.
a.) Calculate the wavelength, in nm, associated with this radiation.
b.) Calculate the energy, in joules, of a single photon associated with this frequency.
4. A laser emits light with a frequency of 4.69×1014 s–1. (a) What is the energy of one photon of the
radiation from this laser? (b) If the laser emits a pulse of energy containing 5.00×1017 photons of this
radiation, what is the total energy of that pulse?
5. The retina of a human eye can detect light when the total radiant energy incident on the retina is at least
4.00×10–17 J. For light of 600.0 nm wavelength, how many photons are required for this much energy?
6. A photochemist determines that 0.0420 moles of particular photons has a total energy of 0.0871 kJ of
energy. What is the frequency and wavelength of the photons.
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7. The average C–C bond energy is 347 kJ/mol. Calculate the wavelength, in nm, of the photon with the
minimum necessary energy to break this bond.
8. From the following list of observations, choose the one that most clearly supports the conclusion that
electrons in atoms have quantized energies.
A)
B)
C)
D)
E)
the emission spectrum of hydrogen
the photoelectric effect
the scattering of alpha particles by metal foil
diffraction
cathode "rays"
A)
B)
C)
D)
E)
the emission spectrum of hydrogen
the photoelectric effect
the scattering of alpha particles by metal foil
diffraction
cathode "rays"
9. From the following list of observations, choose the one that most clearly supports the conclusion that
electromagnetic radiation has wave characteristics.
10. Which of the following statements is (are) true?
A.
B.
C.
D.
An excited atom can return to its ground state by absorbing electromagnetic radiation.
The energy of an atom is increased when electromagnetic radiation is emitted from it.
The energy of electromagnetic radiation increases as its frequency increases.
An electron in the n = 4 state in the hydrogen atom can go to the n = 2 state by emitting
electromagnetic radiation at the appropriate frequency.
E. The frequency and wavelength of electromagnetic radiation are inversely proportional to each other.
11. For which of the following transitions does the light emitted have the longest wavelength?
A)
B)
C)
D)
E)
n = 4 to n = 3
n = 4 to n = 2
n = 3 to n = 1
n = 3 to n = 2
n = 2 to n = 1
12. Which of the following is not determined by the principal quantum number, n, of the electron in a
hydrogen atom?
A) the energy of the electron
B) the size of the corresponding atomic orbital(s)
C) the shape of the corresponding atomic orbital(s)
D) All of the above are determined by n.
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Answers:
1.
2.
3.
4.
5.
𝜈 =𝑐 / 𝜆 = 2.998×108 𝑚/𝑠 × 0.0120×10–9 𝑚 = 2.50×1019 𝐻𝑧 or s–1
0.167 m or 1.67×105 μm.
(a) 425 nm, (b) 4.67×10–19 J/1 photon
(a) 3.11×10–19 J/1 photon, (b) 0.156 J total
Determine the energy of 1 photon:
Ephoton = hc/λ = (6.626×10–34 J∙s)×( 2.998×108 m/s) ÷ 600.0×10–9 nm = 3.31×10–19 J/ photon
Calculate # photons needed to produce given amount of energy:
4.0×10–17 J × ( 1 photon/3.31×10–19 J)
= 1.21×102 photons
6. Calculate # of photons (2.529×1022), divide 87.1 J by # of photons (3.444×10–21 J/photon,
Use E = hν to calculate frequency = 5.20×1012 s–1, wavelength = 5.77×10–5 m or 57.7 um
7. Calculate E per photon from E per mole; 5.762×10–19 J, then use E = hν to get ν = 8.70×1014 s–1 or 345 nm
8.
A
9.
D
10. C, D, and E
11. A
12. C