Chemistry: An Atoms First Approach
Chemistry: An Atoms First Approach
2nd Edition
ISBN: 9781305079243
Author: Steven S. Zumdahl, Susan A. Zumdahl
Publisher: Cengage Learning
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Chapter 2, Problem 43E

Octyl methoxycinoamate and oxybenzone are common ingredients in sunscreen applications. These compounds work by absorbing ultraviolet (UV) B light (wavelength 280-320 nm), the UV light most associated with sunburn symptoms. What frequency range of light do these compounds absorb?

Expert Solution & Answer
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Interpretation Introduction

Interpretation: The frequency range of the UV light that Octyl methoxycinnamate and oxybenzone compounds absorb is to be calculated.

Concept introduction: Frequency of light is defined as the number of waves passes in space during a given interval of time of one second. The frequency of light is measured in the unit of hertz that is also called as cycles per second.

To determine: The frequency range of the UV light that Octyl methoxycinnamate and oxybenzone compounds absorb.

Answer to Problem 43E

Answer

The frequency range of the UV light that Octyl methoxycinnamate and oxybenzone compounds absorb is 1.6×1014 s_1 .

Explanation of Solution

Explanation

The relation between the speed, wavelength and frequency of light is shown below.

The speed of the wave is defined as the product of its wavelength and its frequency. The expression which gives the relationship between the speed, wavelength and frequency of the electromagnetic radiation is as follows,

λν=c

Where,

  • λ is the wavelength of light.
  • c is the speed of light (2.9979×108 m/s ) .
  • ν is the frequency of light.

The frequency of 280 nm light is 1.1×1015s_1 .

Given

The wavelength (λ) range of UV light is 280 nm320 nm .

The conversion of nm to m is done as,

1nm=109 m .

Therefore, the conversion of 280 nm to m is done as,

280 nm=(280×109)m=2.8×107 m .

The speed of light is (2.9979×108 m/s ) .

The frequency of 280 nm light is calculated by using the formula,

ν=cλ

Substitute the value of c and λ in the above expression to calculate the frequency of UV light.

ν=cλ=2.9979×108 m/s2.8×107 m=1.1×1015s_1

Therefore, the upper limit of frequency of the UV light that compound absorbs is 1.1×1015s_1

The frequency of 320 nm light is 9.4×1014s_1 .

The wavelength (λ) range of UV light is 280 nm320 nm .

The conversion of nm to m is done as,

1nm=109 m .

Therefore, the conversion of 320 nm to m is done as,

320 nm=(320×109)m=3.2×107 m .

The speed of light is (2.9979×108 m/s ) .

The frequency of 320 nm light is calculated by using the formula,

ν=cλ

Substitute the value of c and λ in the above expression to calculate the frequency of UV light.

ν=cλ=2.9979×108 m/s3.2×107 m=9.4×1014s_1

Therefore, the lower limit of frequency of the UV light that compound absorbs is 9.4×1014s_1 .

Therefore, the frequency range of the UV light is calculated by the formula,

Frequency range = Upper limitof frequency lower limit of frequency

Substitute the value of upper and lower limit of frequency in the above expression,

Frequency range = Upper limitof frequency Lower limit of frequency=1.1×1015s19.4×1014s1=1.6×1014s1_

Hence, the frequency range of the UV light that Octyl methoxycinnamate and oxybenzone compounds absorb is 1.6×1014 s_1 .

Conclusion

Conclusion

The frequency range of the UV light that Octyl methoxycinnamate and oxybenzone compounds absorb is 1.6×1014 s_1 .

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Chapter 2 Solutions

Chemistry: An Atoms First Approach

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