The number of joules of energy in each liter of space and the number of 1 -mm- wavelength microwave photons the energy would correspond to in each liter.

Question

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Answer 1

Question

Chapter 18, Problem 8P

To determine

The number of joules of energy in each liter of space and the number of 1-mm- wavelength microwave photons the energy would correspond to in each liter.

Expert Solution & Answer

Answer to Problem 8P

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

Explanation of Solution

The critical density of the Universe is 3×10−30 g/cm3 and the dark energy in the universe currently is 68.5%.

Therefore, the dark energy is

0.685×3×10−30 g/cm3=2.055×10−30 g/cm3

Convert g/cm3 to kg/L

2.055×10−30 g/cm3×1000 cm31 L×1 kg1000 g=2.055×10−30 kg/L

The mass of dark energy contains in 1 L of space is 2.055×10−30 kg.

Write the formula to find the value of energy

E=mc2 (I)

Write the expression to find the energy of photon

E=hcλ (II)

Here, E is the energy, h is the Planck’s constant, λ is the wavelength, m is the mass and c is the speed of light.

Substitute 2.055×10−30 kg for m and 3×108 m/s for c in the equation (I) to find the value of E

E=(2.055×10−30 kg)(3×108 m/s)2=1.85×10−13 J

The dark energy present in 1 L is 1.85×10−13 J.

Substitute 6.63×10−34 Js for h, 1 mm(=10−3 m) for λ and 3×108 m/s for c in the equation (II) to find the value of E

E=(6.63×10−34 Js)(3×108 m/s)10−3 m=1.99×10−22 J

The energy of 1-mm- wavelength microwave photons is 1.99×10−22 J.

The 1-mm- wavelength microwave photons in 1 L of space is

=1.85×10−13 J1.99×10−22 J/photon=0.93×109 photons≈1 billion photons

Conclusion:

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

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Answer 2

Question

Chapter 18, Problem 8P

To determine

The number of joules of energy in each liter of space and the number of 1-mm- wavelength microwave photons the energy would correspond to in each liter.

Expert Solution & Answer

Answer to Problem 8P

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

Explanation of Solution

The critical density of the Universe is 3×10−30 g/cm3 and the dark energy in the universe currently is 68.5%.

Therefore, the dark energy is

0.685×3×10−30 g/cm3=2.055×10−30 g/cm3

Convert g/cm3 to kg/L

2.055×10−30 g/cm3×1000 cm31 L×1 kg1000 g=2.055×10−30 kg/L

The mass of dark energy contains in 1 L of space is 2.055×10−30 kg.

Write the formula to find the value of energy

E=mc2 (I)

Write the expression to find the energy of photon

E=hcλ (II)

Here, E is the energy, h is the Planck’s constant, λ is the wavelength, m is the mass and c is the speed of light.

Substitute 2.055×10−30 kg for m and 3×108 m/s for c in the equation (I) to find the value of E

E=(2.055×10−30 kg)(3×108 m/s)2=1.85×10−13 J

The dark energy present in 1 L is 1.85×10−13 J.

Substitute 6.63×10−34 Js for h, 1 mm(=10−3 m) for λ and 3×108 m/s for c in the equation (II) to find the value of E

E=(6.63×10−34 Js)(3×108 m/s)10−3 m=1.99×10−22 J

The energy of 1-mm- wavelength microwave photons is 1.99×10−22 J.

The 1-mm- wavelength microwave photons in 1 L of space is

=1.85×10−13 J1.99×10−22 J/photon=0.93×109 photons≈1 billion photons

Conclusion:

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

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Answer 3

Question

Chapter 18, Problem 8P

To determine

The number of joules of energy in each liter of space and the number of 1-mm- wavelength microwave photons the energy would correspond to in each liter.

Expert Solution & Answer

Answer to Problem 8P

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

Explanation of Solution

The critical density of the Universe is 3×10−30 g/cm3 and the dark energy in the universe currently is 68.5%.

Therefore, the dark energy is

0.685×3×10−30 g/cm3=2.055×10−30 g/cm3

Convert g/cm3 to kg/L

2.055×10−30 g/cm3×1000 cm31 L×1 kg1000 g=2.055×10−30 kg/L

The mass of dark energy contains in 1 L of space is 2.055×10−30 kg.

Write the formula to find the value of energy

E=mc2 (I)

Write the expression to find the energy of photon

E=hcλ (II)

Here, E is the energy, h is the Planck’s constant, λ is the wavelength, m is the mass and c is the speed of light.

Substitute 2.055×10−30 kg for m and 3×108 m/s for c in the equation (I) to find the value of E

E=(2.055×10−30 kg)(3×108 m/s)2=1.85×10−13 J

The dark energy present in 1 L is 1.85×10−13 J.

Substitute 6.63×10−34 Js for h, 1 mm(=10−3 m) for λ and 3×108 m/s for c in the equation (II) to find the value of E

E=(6.63×10−34 Js)(3×108 m/s)10−3 m=1.99×10−22 J

The energy of 1-mm- wavelength microwave photons is 1.99×10−22 J.

The 1-mm- wavelength microwave photons in 1 L of space is

=1.85×10−13 J1.99×10−22 J/photon=0.93×109 photons≈1 billion photons

Conclusion:

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

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Answer 4

Question

Chapter 18, Problem 8P

To determine

The number of joules of energy in each liter of space and the number of 1-mm- wavelength microwave photons the energy would correspond to in each liter.

Expert Solution & Answer

Answer to Problem 8P

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

Explanation of Solution

The critical density of the Universe is 3×10−30 g/cm3 and the dark energy in the universe currently is 68.5%.

Therefore, the dark energy is

0.685×3×10−30 g/cm3=2.055×10−30 g/cm3

Convert g/cm3 to kg/L

2.055×10−30 g/cm3×1000 cm31 L×1 kg1000 g=2.055×10−30 kg/L

The mass of dark energy contains in 1 L of space is 2.055×10−30 kg.

Write the formula to find the value of energy

E=mc2 (I)

Write the expression to find the energy of photon

E=hcλ (II)

Here, E is the energy, h is the Planck’s constant, λ is the wavelength, m is the mass and c is the speed of light.

Substitute 2.055×10−30 kg for m and 3×108 m/s for c in the equation (I) to find the value of E

E=(2.055×10−30 kg)(3×108 m/s)2=1.85×10−13 J

The dark energy present in 1 L is 1.85×10−13 J.

Substitute 6.63×10−34 Js for h, 1 mm(=10−3 m) for λ and 3×108 m/s for c in the equation (II) to find the value of E

E=(6.63×10−34 Js)(3×108 m/s)10−3 m=1.99×10−22 J

The energy of 1-mm- wavelength microwave photons is 1.99×10−22 J.

The 1-mm- wavelength microwave photons in 1 L of space is

=1.85×10−13 J1.99×10−22 J/photon=0.93×109 photons≈1 billion photons

Conclusion:

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 18, Problem 8P

To determine

The number of joules of energy in each liter of space and the number of 1-mm- wavelength microwave photons the energy would correspond to in each liter.

Expert Solution & Answer

Answer to Problem 8P

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

Explanation of Solution

The critical density of the Universe is 3×10−30 g/cm3 and the dark energy in the universe currently is 68.5%.

Therefore, the dark energy is

0.685×3×10−30 g/cm3=2.055×10−30 g/cm3

Convert g/cm3 to kg/L

2.055×10−30 g/cm3×1000 cm31 L×1 kg1000 g=2.055×10−30 kg/L

The mass of dark energy contains in 1 L of space is 2.055×10−30 kg.

Write the formula to find the value of energy

E=mc2 (I)

Write the expression to find the energy of photon

E=hcλ (II)

Here, E is the energy, h is the Planck’s constant, λ is the wavelength, m is the mass and c is the speed of light.

Substitute 2.055×10−30 kg for m and 3×108 m/s for c in the equation (I) to find the value of E

E=(2.055×10−30 kg)(3×108 m/s)2=1.85×10−13 J

The dark energy present in 1 L is 1.85×10−13 J.

Substitute 6.63×10−34 Js for h, 1 mm(=10−3 m) for λ and 3×108 m/s for c in the equation (II) to find the value of E

E=(6.63×10−34 Js)(3×108 m/s)10−3 m=1.99×10−22 J

The energy of 1-mm- wavelength microwave photons is 1.99×10−22 J.

The 1-mm- wavelength microwave photons in 1 L of space is

=1.85×10−13 J1.99×10−22 J/photon=0.93×109 photons≈1 billion photons

Conclusion:

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

Answer 6

Chapter 18, Problem 8P

To determine

The number of joules of energy in each liter of space and the number of 1-mm- wavelength microwave photons the energy would correspond to in each liter.

Expert Solution & Answer

Answer to Problem 8P

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

Explanation of Solution

The critical density of the Universe is 3×10−30 g/cm3 and the dark energy in the universe currently is 68.5%.

Therefore, the dark energy is

0.685×3×10−30 g/cm3=2.055×10−30 g/cm3

Convert g/cm3 to kg/L

2.055×10−30 g/cm3×1000 cm31 L×1 kg1000 g=2.055×10−30 kg/L

The mass of dark energy contains in 1 L of space is 2.055×10−30 kg.

Write the formula to find the value of energy

E=mc2 (I)

Write the expression to find the energy of photon

E=hcλ (II)

Here, E is the energy, h is the Planck’s constant, λ is the wavelength, m is the mass and c is the speed of light.

Substitute 2.055×10−30 kg for m and 3×108 m/s for c in the equation (I) to find the value of E

E=(2.055×10−30 kg)(3×108 m/s)2=1.85×10−13 J

The dark energy present in 1 L is 1.85×10−13 J.

Substitute 6.63×10−34 Js for h, 1 mm(=10−3 m) for λ and 3×108 m/s for c in the equation (II) to find the value of E

E=(6.63×10−34 Js)(3×108 m/s)10−3 m=1.99×10−22 J

The energy of 1-mm- wavelength microwave photons is 1.99×10−22 J.

The 1-mm- wavelength microwave photons in 1 L of space is

=1.85×10−13 J1.99×10−22 J/photon=0.93×109 photons≈1 billion photons

Conclusion:

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

Answer 7

Chapter 18, Problem 8P

To determine

The number of joules of energy in each liter of space and the number of 1-mm- wavelength microwave photons the energy would correspond to in each liter.

Answer 8

Expert Solution & Answer

Answer to Problem 8P

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

The critical density of the Universe is 3×10−30 g/cm3 and the dark energy in the universe currently is 68.5%.

Therefore, the dark energy is

0.685×3×10−30 g/cm3=2.055×10−30 g/cm3

Convert g/cm3 to kg/L

2.055×10−30 g/cm3×1000 cm31 L×1 kg1000 g=2.055×10−30 kg/L

The mass of dark energy contains in 1 L of space is 2.055×10−30 kg.

Write the formula to find the value of energy

E=mc2 (I)

Write the expression to find the energy of photon

E=hcλ (II)

Here, E is the energy, h is the Planck’s constant, λ is the wavelength, m is the mass and c is the speed of light.

Substitute 2.055×10−30 kg for m and 3×108 m/s for c in the equation (I) to find the value of E

E=(2.055×10−30 kg)(3×108 m/s)2=1.85×10−13 J

The dark energy present in 1 L is 1.85×10−13 J.

Substitute 6.63×10−34 Js for h, 1 mm(=10−3 m) for λ and 3×108 m/s for c in the equation (II) to find the value of E

E=(6.63×10−34 Js)(3×108 m/s)10−3 m=1.99×10−22 J

The energy of 1-mm- wavelength microwave photons is 1.99×10−22 J.

The 1-mm- wavelength microwave photons in 1 L of space is

=1.85×10−13 J1.99×10−22 J/photon=0.93×109 photons≈1 billion photons

Conclusion:

The number of joules of energy in each liter of space is 1.85×10−13 J and the energy would correspond to 1 billion 1-mm- wavelength microwave photons in each liter.

Answer 12

Ch. 18 - Why do astronomers think that the Universe is...Ch. 18 - What is meant by the age of the Universe? How old...Ch. 18 - Prob. 3QFR Ch. 18 - What is Olbers paradox?Ch. 18 - Prob. 5QFR Ch. 18 - Prob. 6QFR Ch. 18 - Prob. 7QFR Ch. 18 - Prob. 8QFR Ch. 18 - Prob. 9QFR Ch. 18 - Prob. 10QFR

The number of joules of energy in each liter of space and the number of 1 -mm- wavelength microwave photons the energy would correspond to in each liter.

Concept explainers

The number of joules of energy in each liter of space and the number of 1-mm- wavelength microwave photons the energy would correspond to in each liter.

Answer to Problem 8P

Explanation of Solution

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Chapter 18 Solutions