CHEM 1161: Light and Spectroscopy
Frequency,
 (Hz)
Questions:
1. What is the approximate wavelength () of a microwave? ___________
2. What is the approximate frequency () of a microwave? ___________
3. What is the approximate wavelength () of an X-ray? ___________
4. What is the approximate frequency () of an X-ray? ___________
5. Based on your answers for Q1-4 above, what is the relationship between frequency and
wavelength?
Mathematical Relationships with Light:
𝑐
a) Frequency: 𝜈 = 𝜆
b) Energy: 𝐸 = ℎ𝜈
c) Speed of light: 𝑐 = 3.00 × 108 𝑚/𝑠
d) Planck’s constant: ℎ = 6.626 × 10−34 𝐽 ∙ 𝑠
Critical Thinking:
6. Looking at Equation a), what is the relationship between frequency and wavelength? Is this
consistent with your answer for Q5?
7. Looking at Equation b), what is the relationship between energy and frequency?
8. Combine Equations a) and b) to form a relationship between energy and wavelength. How
are these two properties related?
Created by: Dr. Dan Matthew
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CHEM 1161: Light and Spectroscopy
Sample Problems:
9. For each of the pairs of photon descriptions, determine which photon has the greatest
frequency.
a. Comparing wavelengths:
i. A photon with a wavelength of 950 nm.
ii. A photon with a wavelength of 450 nm.
b. Comparing regions of the electromagnetic spectrum:
i. A photon produced by an X-ray machine.
ii. A photon produced by a microwave oven.
c. Comparing energies:
i. A photon with an energy of 1 × 10−19 𝐽.
ii. A photon with an energy of 1 × 10−25 𝐽.
d. Comparing colors of the visible spectrum:
i. An orange photon.
ii. A blue photon.
10. The photochemical reaction that initiates the production of smog involves the decomposition
of NO molecules. A photon capable of breaking this N–O bond has a wavelength of 191 nm.
a. Without calculating anything, how much energy do you expect a single photon to have?
(Circle your answer)
𝐸 ≪ 1𝐽
𝐸 ≈1𝐽
𝐸 ≫1𝐽
b. Calculate the amount of energy, in Joules, of one photon of wavelength 191 nm.
c. How many photons of wavelength 191 nm would be required to decompose (i.e., break
all N–O bonds) 0.51 mg of NO?
11. On average, 3.0 µmole of photons with a wavelength of 400.0nm (blue light) fall on 1m2 of
Earth’s surface in 1.0 second. What is the total energy of this amount of light in Joules?
Created by: Dr. Dan Matthew
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CHEM 1161: Light and Spectroscopy
Electronic Spectroscopy:
For these problems, you will use the equation for the energy of a hydrogen atom when its
electron is in a given 𝑛 state:
1
𝐸𝑛 = −2.18 × 10−18 𝐽 × 2
𝑛
To find the change in energy between two of these states (e.g., when a hydrogen atom absorbs
or emits a photon), you simply calculate:
1
1
Δ𝐸 = 𝐸𝑓 − 𝐸𝑖 = −𝑅𝐻 ( 2 − 2 )
𝑛𝑓 𝑛𝑖
12. Calculate the amount of energy a hydrogen atom has when its electron is sitting in the 𝑛 = 1
state.
13. Calculate the amount of energy a hydrogen atom has when its electron is sitting in the 𝑛 = 3
state.
14. Calculate how much energy a hydrogen atom gains when it absorbs enough energy to excite
it from the 𝑛 = 1 state to the 𝑛 = 3 state.
15. The energy described in the problem above can be imparted into the atom via a photon of
light energy equal to the needed energy for that transition (no more, no less). Calculate the
wavelength of light that corresponds to the energy you calculated in the question above. This
is the wavelength of the photon that a hydrogen atom can absorb to excite it from the ground
state (𝑛 = 1) to the excited 𝑛 = 3 state.
16. Calculate the wavelength, in nm, of the photon emitted by a hydrogen atom when is relaxes
from 𝑛 = 5 to 𝑛 = 2.
Created by: Dr. Dan Matthew
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