   # Assume your eyes receive a signal consisting of blue light, ʎ = 470 nm. The energy of the signal is 2.50 × 10 –14 J. How many photons reach your eyes? ### 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, Problem 58GQ
Textbook Problem
241 views

## Assume your eyes receive a signal consisting of blue light, ʎ = 470 nm. The energy of the signal is 2.50 × 10–14 J. How many photons reach your eyes?

Interpretation Introduction

Interpretation: The number of photons of reaching our eyes is to be calculated.

Concept introduction:

• Electromagnetic radiations are a type of energy surrounding us. They are of different types like radio waves, IR, UV, X-ray etc.
• The blue light is in the visible region of electromagnetic radiation where it lies in the wavelength of 400nm and 700nm
• 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

Given,

Planck'sconstant,h=6.626×1034J.sThe speed of light,c=2.998×108m/sWavelength ultraviolet light =470nm=4.7 ×107mThe total energy of the signal=2.50×1014J

The frequency of ultraviolet light is,

ν=cλ                                        (a)

The energy per photon of ultraviolet light is,

E=                                        (b)

Combining (a) and (b)

E=hcλ

Substituting the values to the above equation,

E=(6.626×1034J

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