Bundle: Physical Chemistry, 2nd + Student Solutions Manual
Bundle: Physical Chemistry, 2nd + Student Solutions Manual
2nd Edition
ISBN: 9781285257594
Author: David W. Ball
Publisher: Cengage Learning
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Chapter 9, Problem 9.40E
Interpretation Introduction

Interpretation:

The energy of a single photon in joules and the energy of a mole of photons in J/mol for light having the given wavelengths are to be calculated. Whether the calculated energies explain the relative danger of electromagnetic radiation of differing wavelengths or not is to be stated.

Concept introduction:

A small packet of energy is known as the quanta. Light is emitted in the form of quanta or photons. The Planck’s law gives the relation between the energy and wavelength, frequency and wavenumber.

Expert Solution & Answer
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Answer to Problem 9.40E

The energy of single photon in joules and the energy of a mole of photons in J/mol for light having wavelength of 10m (radio and TV waves) is 1.99×1026J and 1.2×102J/mol, 10.0cm (microwaves) is 1.99×1023J and 1.2J/mol, 10microns (infrared range) is 1.99×1020J and 1.2×104J/mol, 550nm (green light) is 3.6×1019J and 2.4×105J/mol, 300nm (ultraviolet) is 6.6×1019J and 4.0×105J/mol and 1.00A (X rays) is 1.99×1015J and 1.2×109J/mol.

The shorter wavelength radiations are more dangerous because these radiations transmit more energy.

Explanation of Solution

The energy of single photon in joules is calculated by the formula,

E=hν The formula can be written as follows:

E=hcλ(1)

Where,

h is the planks constant.

c is the velocity of light.

λ is the wave length.

The energy of a mole of photons in J/mol is calculated by the formula,

E=NAhcλ(2)

Where,

NA is the Avogadro number.

E is the energy of a mole of photon in J/mol.

The given wavelength of light is 10m (radio and TV waves).

Substitute the value of λ and c in the equation (1)

E=hcλ=(6.626×1034Js)(3.0×108ms1)10m=1.99×1026J

Thus, the energy of single photon in joules is 1.99×1026J.

Substitute the value of λ and c in the equation (2).

E=(6.022×1023mol1)×(6.626×1034Js)(3.0×108ms1)10mE=1.2×102J/mol

Thus, the energy of a mole of photons in J/mol is 1.2×102J/mol.

The given wavelength of light is 10.0cm (microwaves).

Substitute the value of λ and c in the equation (1)

E=hcλ=(6.626×1034Js)(3.0×108ms1)10.0cm×(102m10.0cm)=1.99×1023J

Thus, the energy of single photon in joules is 1.99×1024J.

Substitute the value of λ and c in the equation (2).

E=(6.022×1023mol1)×(6.626×1034Js)(3.0×108ms1)10.0cm×(102m10.0cm)E=1.2J/mol

Thus, the energy of a mole of photons in J/mol is 1.2J/mol.

The given wavelength of light is 10microns (infrared range).

Substitute the value of λ and c in the equation (1)

E=hcλ=(6.626×1034Js)(3.0×108ms1)10microns×(106m1microns)=1.99×1020J

Thus, the energy of single photon in joules is 1.99×1020J.

Substitute the value of λ and c in the equation (2).

E=(6.022×1023mol1)×(6.626×1034Js)(3.0×108ms1)10microns×(106m1microns)E=1.2×104J/mol

Thus, the energy of a mole of photons in J/mol is 1.2×104J/mol.

The given wavelength of light is 550nm (green light).

Substitute the value of λ and c in the equation (1)

E=hcλ=(6.626×1034Js)(3.0×108ms1)550.0nm×(109m1nm)=3.6×1019J

Thus, the energy of single photon in joules is 3.6×1019J.

Substitute the value of λ and c in the equation (2).

E=(6.022×1023mol1)×(6.626×1034Js)(3.0×108ms1)550.0nm×(109m1nm)E=2.4×105J/mol

Thus, the energy of a mole of photons in J/mol is 2.4×105J/mol.

The given wavelength of light is 300nm (ultraviolet).

Substitute the value of λ and c in the equation (1)

E=hcλ=(6.626×1034Js)(3.0×108ms1)300nm×(109m1nm)=6.6×1019J

Thus, the energy of single photon in joules is 6.6×1019J.

Substitute the value of λ and c in the equation (2).

E=(6.022×1023mol1)×(6.626×1034Js)(3.0×108ms1)300nm×(109m1nm)E=4.0×105J/mol

Thus, the energy of a mole of photons in J/mol is 4.0×105J/mol.

The given wavelength of light is 1.00A (X rays).

Substitute the value of λ and c in the equation (1)

E=hcλ=(6.626×1034Js)(3.0×108ms1)1.00A°×(1010m1.00A°)=1.99×1015J

Thus, the energy of single photon in joules is 1.99×1015J.

Substitute the value of λ and c in the equation (2).

E=(6.022×1023mol1)×(6.626×1034Js)(3.0×108ms1)1.00A°×(1010m1.00A°)E=1.2×109J/mol

Thus, the energy of a mole of photons in J/mol is 1.2×109J/mol.

It is observed from the above calculated values that the energy of per mole for shorter wavelength radiations is higher than the energy of per mole for longer wavelength radiations. Thus, the shorter wavelength radiations are more dangerous.

Conclusion

The energy of single photon in joules and the energy of a mole of photons in J/mol for light having wavelength of 10m (radio and TV waves) is 1.99×1026J and 1.2×102J/mol, 10.0cm (microwaves) is 1.99×1023J and 1.2J/mol, 10microns (infrared range) is 1.99×1020J and 1.2×104J/mol, 550nm (green light) is 3.6×1019J and 2.4×105J/mol, 300nm (ultraviolet) is 6.6×1019J and 4.0×105J/mol and 1.00A (X rays) is 1.99×1015J and 1.2×109J/mol.

The shorter wavelength radiations are more dangerous because these radiations transmit more energy.

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Chapter 9 Solutions

Bundle: Physical Chemistry, 2nd + Student Solutions Manual

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