   # Various manufacturers have developed mixtures of compounds that protect skin from UV-A (400−315 nm) and UV-B (315−280 nm) radiation. These sunscreens are given "sun protection factor" (SPF) labels that indicate how long the user can stay in the Sun without burning. 1. Calculate the energy of a mole of photons of UV-B light with a wavelength of 310 nm. (a) 3.9 × 10 s J/mol (b) 1.2 × 10 s J/mol (c) 0.00039 J/mol ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 6.2, Problem 1RC
Textbook Problem
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## Various manufacturers have developed mixtures of compounds that protect skin from UV-A (400−315 nm) and UV-B (315−280 nm) radiation. These sunscreens are given "sun protection factor" (SPF) labels that indicate how long the user can stay in the Sun without burning.1. Calculate the energy of a mole of photons of UV-B light with a wavelength of 310 nm. (a) 3.9 × 10s J/mol (b) 1.2 × 10s J/mol (c) 0.00039 J/mol

Interpretation Introduction

Interpretation: The energy of a mole of photons of UV-B light is to be determined from the given option.

Concept introduction:

• Planck’s equation,

E=where, E=energyh=Planck'sconstantν=frequency

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

• The frequency of the light is inversely proportional to its wavelength.

ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

### Explanation of Solution

Reason for correct option

Given,

The wavelength of UV-B light is 310 nm=3.1 ×107m .

The energy per photon is,

E= (a)

The frequency per mole of photons is,

ν=cλ (b)

Combining equation (a) and (b),

The energy per photon is,

E=hcλ

Substituting the values to the above equation,

E=hcλ=6.626×1034J.s×2.998×108m/s3.1 ×107m=6

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