   Chapter 6, Problem 5PS

Chapter
Section
Textbook Problem

Green light has a wavelength of 5.0× 102 nm. What is the energy, in joules, of one photon of green light? What is the energy, in joules, of 1.0 mol of photons of green light?

Interpretation Introduction

Interpretation: The energy of one photon and energy of 1.0mol of photons of green light is to be calculated.

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

The energy of one photon and energy of 1.0mol of photons of green line is calculated below.

Given,

The wavelength of absorption line of hydrogen is 500 nm=5.0 ×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 calculated in joules,

E=hcλ

Substituting the values to the above equation,

E=6.626×1034J.s×2.998×108m/s5

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