The mass of neutrinos in the unit of kilograms and also as a fraction of the mass of the electron, if the Hubble constant is about 73 km/s/Mpc , critical density ρ c is 1 × 10 − 26 kg/m 3 and its average density is about 0.20 ρ c . The average density of a neutrino in space is about 100 neutrino/cm 3 .

Question

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Answer 1

Question

Chapter 26, Problem 46Q

(a)

To determine

The mass of neutrinos in the unit of kilograms and also as a fraction of the mass of the electron, if the Hubble constant is about 73 km/s/Mpc, critical density ρc is 1×10−26 kg/m3 and its average density is about 0.20 ρc. The average density of a neutrino in space is about 100 neutrino/cm3.

(a)

Expert Solution

Answer to Problem 46Q

Solution:

2×10−35 kg, 2.1×10−5

Explanation of Solution

Given data:

The Hubble constant has a value of 73 km/s/Mpc.

The critical density has a value of 1×10−26 kg/m3.

The average density of dark matter is 0.20ρc.

The average density of neutrino throughout the space is 100 neutrino/cm3.

Formula used:

The relation between the Hubble law and critical density is presented below.

ρc= 3H028πG

In the equation, G is the universal constant whose value is 6.67×10−11 N⋅m2/kg, H0 is the Hubble constant and ρc is the critical density.

Explanation:

Convert the value of H0 into seconds.

H0= 73 km/s/Mpc=73 kms⋅Mpc(1 Mpc3.08×1019 km)= 2.37×10−18 s−1

Recall, the expression for critical density.

ρc= 3H028πG

Substitute 2.37×10−18 s−1 for H0 and 6.67×10−11 N⋅m2/kg for G.

ρc= 3(2.37×10−18 s−1)2 8π(6.67×10−11 N⋅m2/kg)=1×10−26 kg/m3

Average density of dark matter is 0.20ρc.

ρdm=0.20ρc

In the relation above, ρdm is the average density of dark matter.

Substitute 1×10−26 kg/m3 for ρc.

ρdm= 0.20(1×10−26 kg/m3)= 2×10−27 kg/m3

The average density of neutrino throughout the space is 100 neutrino/cm3. So, the number of the neutrino in a cubic meter of space is obtained as follows.

n=100 cm−3(106 cm31 m3)=108 m−3

Therefore, the mass of the neutrino is obtained from the following calculation.

m=ρdmn

Substitute 2×10−27 kg/m3 for ρdm and 108 m−3 for n.

m=2×10−27 kg/m3108 m−3=2×10−35 kg

The mass in terms of mass of electron (me) which has a value of 9.1×10−31 kg. Thus, the above value calculated in terms of electron mass as presented below.

m=2×10−35 kg(1 me9.1×10−31 kg)=2.2×10−5 me

Conclusion:

The mass of the neutrino in kilograms is 2×10−35 kg and as a fraction of mass of electron is 2.2×10−5.

(b)

To determine

The reason due to which astronomers do not consider massive neutrinos as the prominent type of dark matter.

(b)

Expert Solution

Answer to Problem 46Q

Solution:

The cold matter is the dominant form of dark matter. This suggests that massive neutrinos, which are hot, are not the dominant type of dark matter in the universe.

Explanation of Solution

Introduction:

Dark matter: Dark matter does not emit electromagnetic radiations and thus cannot be detected directly. It constitutes 80% of the universe. It is thought to be non-baryonic in nature which means it is composed of some undiscovered subatomic particles.

Explanation:

Example of hot dark matters are Neutrinos because they comprise of lightweight particles which travel at high speed. Cold matter, on the other hand, comprises of massive particles at low speed.

Massless neutrinos, like photons, always travel at the speed of light. However, neutrinos possess a small mass and the gravitational pull on surrounding matter. This graviational pull could lead to the formation of galaxies.

In cold matter, the formation of the galaxy takes place from bottom to up means the intersection between filaments occurs. These filaments merge together into galaxies. These galaxies are converted into clusters of galaxies, after which they become superclusters.

On the other hand, hot matter galaxies follow a top to bottom sequence of formation. Observation from the remote galaxies suggests that the formation of matter occurs by “bottom-up” scenario. Thus, hot matter such as massive neutrino is not responsible for formation of galaxies and hence is not the dominant form of dark matter.

Conclusion:

From this observation, it is concluded that the prominent form of dark matter is cold. This suggests that massive neutrinos (which are hot) do not constitute prominent type of dark matter present in the universe.

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Students have asked these similar questions

The mass of the neutrino plays an important role in the universe. Suppose the mass of two neutrinos in the universe is 4.8×10-³5 kg and the current Hubble’s constant is 72 km/s/Mpc. The critical density of the universe is five times the average density of the universe. Estimate the number of neutrons present per cubic meter in the universe. (a) 2.1×10⁹ (b) 4.1×10² (c) 1.1x10° (d) 8.1×107

a) Define the term “standard candle” as used in cosmology b). The flux is defined as f(Dlum) = L /4πD2lum , where L is the absolute luminosity and Dlum is the distance to the radiation source (you may assume z ≪ 1). Assume that we have measured the flux to be f = 7.234 10−23Wm−2 and the absolute luminosity is given by L = 3.828 1026W. Calculate the luminosity distance Dlum to the object in Mpc. c). Calculate the distance modulus µ for the object of the previous subquestion. Show that the distance modulus µ can be written as given in image

With a Hubble constant of 70 km/sec/Mpc, the critical density would be 1.4 g/cc. 9 × 10-27 kg/m3. 6.23 × 10-23 g/mole. 4 × 10-36 g/cc. 3 × 10-31 g/cc.

Answer 2

Question

Chapter 26, Problem 46Q

(a)

To determine

The mass of neutrinos in the unit of kilograms and also as a fraction of the mass of the electron, if the Hubble constant is about 73 km/s/Mpc, critical density ρc is 1×10−26 kg/m3 and its average density is about 0.20 ρc. The average density of a neutrino in space is about 100 neutrino/cm3.

(a)

Expert Solution

Answer to Problem 46Q

Solution:

2×10−35 kg, 2.1×10−5

Explanation of Solution

Given data:

The Hubble constant has a value of 73 km/s/Mpc.

The critical density has a value of 1×10−26 kg/m3.

The average density of dark matter is 0.20ρc.

The average density of neutrino throughout the space is 100 neutrino/cm3.

Formula used:

The relation between the Hubble law and critical density is presented below.

ρc= 3H028πG

In the equation, G is the universal constant whose value is 6.67×10−11 N⋅m2/kg, H0 is the Hubble constant and ρc is the critical density.

Explanation:

Convert the value of H0 into seconds.

H0= 73 km/s/Mpc=73 kms⋅Mpc(1 Mpc3.08×1019 km)= 2.37×10−18 s−1

Recall, the expression for critical density.

ρc= 3H028πG

Substitute 2.37×10−18 s−1 for H0 and 6.67×10−11 N⋅m2/kg for G.

ρc= 3(2.37×10−18 s−1)2 8π(6.67×10−11 N⋅m2/kg)=1×10−26 kg/m3

Average density of dark matter is 0.20ρc.

ρdm=0.20ρc

In the relation above, ρdm is the average density of dark matter.

Substitute 1×10−26 kg/m3 for ρc.

ρdm= 0.20(1×10−26 kg/m3)= 2×10−27 kg/m3

The average density of neutrino throughout the space is 100 neutrino/cm3. So, the number of the neutrino in a cubic meter of space is obtained as follows.

n=100 cm−3(106 cm31 m3)=108 m−3

Therefore, the mass of the neutrino is obtained from the following calculation.

m=ρdmn

Substitute 2×10−27 kg/m3 for ρdm and 108 m−3 for n.

m=2×10−27 kg/m3108 m−3=2×10−35 kg

The mass in terms of mass of electron (me) which has a value of 9.1×10−31 kg. Thus, the above value calculated in terms of electron mass as presented below.

m=2×10−35 kg(1 me9.1×10−31 kg)=2.2×10−5 me

Conclusion:

The mass of the neutrino in kilograms is 2×10−35 kg and as a fraction of mass of electron is 2.2×10−5.

(b)

To determine

The reason due to which astronomers do not consider massive neutrinos as the prominent type of dark matter.

(b)

Expert Solution

Answer to Problem 46Q

Solution:

The cold matter is the dominant form of dark matter. This suggests that massive neutrinos, which are hot, are not the dominant type of dark matter in the universe.

Explanation of Solution

Introduction:

Dark matter: Dark matter does not emit electromagnetic radiations and thus cannot be detected directly. It constitutes 80% of the universe. It is thought to be non-baryonic in nature which means it is composed of some undiscovered subatomic particles.

Explanation:

Example of hot dark matters are Neutrinos because they comprise of lightweight particles which travel at high speed. Cold matter, on the other hand, comprises of massive particles at low speed.

Massless neutrinos, like photons, always travel at the speed of light. However, neutrinos possess a small mass and the gravitational pull on surrounding matter. This graviational pull could lead to the formation of galaxies.

In cold matter, the formation of the galaxy takes place from bottom to up means the intersection between filaments occurs. These filaments merge together into galaxies. These galaxies are converted into clusters of galaxies, after which they become superclusters.

On the other hand, hot matter galaxies follow a top to bottom sequence of formation. Observation from the remote galaxies suggests that the formation of matter occurs by “bottom-up” scenario. Thus, hot matter such as massive neutrino is not responsible for formation of galaxies and hence is not the dominant form of dark matter.

Conclusion:

From this observation, it is concluded that the prominent form of dark matter is cold. This suggests that massive neutrinos (which are hot) do not constitute prominent type of dark matter present in the universe.

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Answer 3

Question

Chapter 26, Problem 46Q

(a)

To determine

The mass of neutrinos in the unit of kilograms and also as a fraction of the mass of the electron, if the Hubble constant is about 73 km/s/Mpc, critical density ρc is 1×10−26 kg/m3 and its average density is about 0.20 ρc. The average density of a neutrino in space is about 100 neutrino/cm3.

(a)

Expert Solution

Answer to Problem 46Q

Solution:

2×10−35 kg, 2.1×10−5

Explanation of Solution

Given data:

The Hubble constant has a value of 73 km/s/Mpc.

The critical density has a value of 1×10−26 kg/m3.

The average density of dark matter is 0.20ρc.

The average density of neutrino throughout the space is 100 neutrino/cm3.

Formula used:

The relation between the Hubble law and critical density is presented below.

ρc= 3H028πG

In the equation, G is the universal constant whose value is 6.67×10−11 N⋅m2/kg, H0 is the Hubble constant and ρc is the critical density.

Explanation:

Convert the value of H0 into seconds.

H0= 73 km/s/Mpc=73 kms⋅Mpc(1 Mpc3.08×1019 km)= 2.37×10−18 s−1

Recall, the expression for critical density.

ρc= 3H028πG

Substitute 2.37×10−18 s−1 for H0 and 6.67×10−11 N⋅m2/kg for G.

ρc= 3(2.37×10−18 s−1)2 8π(6.67×10−11 N⋅m2/kg)=1×10−26 kg/m3

Average density of dark matter is 0.20ρc.

ρdm=0.20ρc

In the relation above, ρdm is the average density of dark matter.

Substitute 1×10−26 kg/m3 for ρc.

ρdm= 0.20(1×10−26 kg/m3)= 2×10−27 kg/m3

The average density of neutrino throughout the space is 100 neutrino/cm3. So, the number of the neutrino in a cubic meter of space is obtained as follows.

n=100 cm−3(106 cm31 m3)=108 m−3

Therefore, the mass of the neutrino is obtained from the following calculation.

m=ρdmn

Substitute 2×10−27 kg/m3 for ρdm and 108 m−3 for n.

m=2×10−27 kg/m3108 m−3=2×10−35 kg

The mass in terms of mass of electron (me) which has a value of 9.1×10−31 kg. Thus, the above value calculated in terms of electron mass as presented below.

m=2×10−35 kg(1 me9.1×10−31 kg)=2.2×10−5 me

Conclusion:

The mass of the neutrino in kilograms is 2×10−35 kg and as a fraction of mass of electron is 2.2×10−5.

(b)

To determine

The reason due to which astronomers do not consider massive neutrinos as the prominent type of dark matter.

(b)

Expert Solution

Answer to Problem 46Q

Solution:

The cold matter is the dominant form of dark matter. This suggests that massive neutrinos, which are hot, are not the dominant type of dark matter in the universe.

Explanation of Solution

Introduction:

Dark matter: Dark matter does not emit electromagnetic radiations and thus cannot be detected directly. It constitutes 80% of the universe. It is thought to be non-baryonic in nature which means it is composed of some undiscovered subatomic particles.

Explanation:

Example of hot dark matters are Neutrinos because they comprise of lightweight particles which travel at high speed. Cold matter, on the other hand, comprises of massive particles at low speed.

Massless neutrinos, like photons, always travel at the speed of light. However, neutrinos possess a small mass and the gravitational pull on surrounding matter. This graviational pull could lead to the formation of galaxies.

In cold matter, the formation of the galaxy takes place from bottom to up means the intersection between filaments occurs. These filaments merge together into galaxies. These galaxies are converted into clusters of galaxies, after which they become superclusters.

On the other hand, hot matter galaxies follow a top to bottom sequence of formation. Observation from the remote galaxies suggests that the formation of matter occurs by “bottom-up” scenario. Thus, hot matter such as massive neutrino is not responsible for formation of galaxies and hence is not the dominant form of dark matter.

Conclusion:

From this observation, it is concluded that the prominent form of dark matter is cold. This suggests that massive neutrinos (which are hot) do not constitute prominent type of dark matter present in the universe.

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

Answer 4

Question

Chapter 26, Problem 46Q

(a)

To determine

The mass of neutrinos in the unit of kilograms and also as a fraction of the mass of the electron, if the Hubble constant is about 73 km/s/Mpc, critical density ρc is 1×10−26 kg/m3 and its average density is about 0.20 ρc. The average density of a neutrino in space is about 100 neutrino/cm3.

(a)

Expert Solution

Answer to Problem 46Q

Solution:

2×10−35 kg, 2.1×10−5

Explanation of Solution

Given data:

The Hubble constant has a value of 73 km/s/Mpc.

The critical density has a value of 1×10−26 kg/m3.

The average density of dark matter is 0.20ρc.

The average density of neutrino throughout the space is 100 neutrino/cm3.

Formula used:

The relation between the Hubble law and critical density is presented below.

ρc= 3H028πG

In the equation, G is the universal constant whose value is 6.67×10−11 N⋅m2/kg, H0 is the Hubble constant and ρc is the critical density.

Explanation:

Convert the value of H0 into seconds.

H0= 73 km/s/Mpc=73 kms⋅Mpc(1 Mpc3.08×1019 km)= 2.37×10−18 s−1

Recall, the expression for critical density.

ρc= 3H028πG

Substitute 2.37×10−18 s−1 for H0 and 6.67×10−11 N⋅m2/kg for G.

ρc= 3(2.37×10−18 s−1)2 8π(6.67×10−11 N⋅m2/kg)=1×10−26 kg/m3

Average density of dark matter is 0.20ρc.

ρdm=0.20ρc

In the relation above, ρdm is the average density of dark matter.

Substitute 1×10−26 kg/m3 for ρc.

ρdm= 0.20(1×10−26 kg/m3)= 2×10−27 kg/m3

The average density of neutrino throughout the space is 100 neutrino/cm3. So, the number of the neutrino in a cubic meter of space is obtained as follows.

n=100 cm−3(106 cm31 m3)=108 m−3

Therefore, the mass of the neutrino is obtained from the following calculation.

m=ρdmn

Substitute 2×10−27 kg/m3 for ρdm and 108 m−3 for n.

m=2×10−27 kg/m3108 m−3=2×10−35 kg

The mass in terms of mass of electron (me) which has a value of 9.1×10−31 kg. Thus, the above value calculated in terms of electron mass as presented below.

m=2×10−35 kg(1 me9.1×10−31 kg)=2.2×10−5 me

Conclusion:

The mass of the neutrino in kilograms is 2×10−35 kg and as a fraction of mass of electron is 2.2×10−5.

(b)

To determine

The reason due to which astronomers do not consider massive neutrinos as the prominent type of dark matter.

(b)

Expert Solution

Answer to Problem 46Q

Solution:

The cold matter is the dominant form of dark matter. This suggests that massive neutrinos, which are hot, are not the dominant type of dark matter in the universe.

Explanation of Solution

Introduction:

Dark matter: Dark matter does not emit electromagnetic radiations and thus cannot be detected directly. It constitutes 80% of the universe. It is thought to be non-baryonic in nature which means it is composed of some undiscovered subatomic particles.

Explanation:

Example of hot dark matters are Neutrinos because they comprise of lightweight particles which travel at high speed. Cold matter, on the other hand, comprises of massive particles at low speed.

Massless neutrinos, like photons, always travel at the speed of light. However, neutrinos possess a small mass and the gravitational pull on surrounding matter. This graviational pull could lead to the formation of galaxies.

In cold matter, the formation of the galaxy takes place from bottom to up means the intersection between filaments occurs. These filaments merge together into galaxies. These galaxies are converted into clusters of galaxies, after which they become superclusters.

On the other hand, hot matter galaxies follow a top to bottom sequence of formation. Observation from the remote galaxies suggests that the formation of matter occurs by “bottom-up” scenario. Thus, hot matter such as massive neutrino is not responsible for formation of galaxies and hence is not the dominant form of dark matter.

Conclusion:

From this observation, it is concluded that the prominent form of dark matter is cold. This suggests that massive neutrinos (which are hot) do not constitute prominent type of dark matter present in the universe.

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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 26, Problem 46Q

(a)

To determine

The mass of neutrinos in the unit of kilograms and also as a fraction of the mass of the electron, if the Hubble constant is about 73 km/s/Mpc, critical density ρc is 1×10−26 kg/m3 and its average density is about 0.20 ρc. The average density of a neutrino in space is about 100 neutrino/cm3.

(a)

Expert Solution

Answer to Problem 46Q

Solution:

2×10−35 kg, 2.1×10−5

Explanation of Solution

Given data:

The Hubble constant has a value of 73 km/s/Mpc.

The critical density has a value of 1×10−26 kg/m3.

The average density of dark matter is 0.20ρc.

The average density of neutrino throughout the space is 100 neutrino/cm3.

Formula used:

The relation between the Hubble law and critical density is presented below.

ρc= 3H028πG

In the equation, G is the universal constant whose value is 6.67×10−11 N⋅m2/kg, H0 is the Hubble constant and ρc is the critical density.

Explanation:

Convert the value of H0 into seconds.

H0= 73 km/s/Mpc=73 kms⋅Mpc(1 Mpc3.08×1019 km)= 2.37×10−18 s−1

Recall, the expression for critical density.

ρc= 3H028πG

Substitute 2.37×10−18 s−1 for H0 and 6.67×10−11 N⋅m2/kg for G.

ρc= 3(2.37×10−18 s−1)2 8π(6.67×10−11 N⋅m2/kg)=1×10−26 kg/m3

Average density of dark matter is 0.20ρc.

ρdm=0.20ρc

In the relation above, ρdm is the average density of dark matter.

Substitute 1×10−26 kg/m3 for ρc.

ρdm= 0.20(1×10−26 kg/m3)= 2×10−27 kg/m3

The average density of neutrino throughout the space is 100 neutrino/cm3. So, the number of the neutrino in a cubic meter of space is obtained as follows.

n=100 cm−3(106 cm31 m3)=108 m−3

Therefore, the mass of the neutrino is obtained from the following calculation.

m=ρdmn

Substitute 2×10−27 kg/m3 for ρdm and 108 m−3 for n.

m=2×10−27 kg/m3108 m−3=2×10−35 kg

The mass in terms of mass of electron (me) which has a value of 9.1×10−31 kg. Thus, the above value calculated in terms of electron mass as presented below.

m=2×10−35 kg(1 me9.1×10−31 kg)=2.2×10−5 me

Conclusion:

The mass of the neutrino in kilograms is 2×10−35 kg and as a fraction of mass of electron is 2.2×10−5.

(b)

To determine

The reason due to which astronomers do not consider massive neutrinos as the prominent type of dark matter.

(b)

Expert Solution

Answer to Problem 46Q

Solution:

The cold matter is the dominant form of dark matter. This suggests that massive neutrinos, which are hot, are not the dominant type of dark matter in the universe.

Explanation of Solution

Introduction:

Dark matter: Dark matter does not emit electromagnetic radiations and thus cannot be detected directly. It constitutes 80% of the universe. It is thought to be non-baryonic in nature which means it is composed of some undiscovered subatomic particles.

Explanation:

Example of hot dark matters are Neutrinos because they comprise of lightweight particles which travel at high speed. Cold matter, on the other hand, comprises of massive particles at low speed.

Massless neutrinos, like photons, always travel at the speed of light. However, neutrinos possess a small mass and the gravitational pull on surrounding matter. This graviational pull could lead to the formation of galaxies.

In cold matter, the formation of the galaxy takes place from bottom to up means the intersection between filaments occurs. These filaments merge together into galaxies. These galaxies are converted into clusters of galaxies, after which they become superclusters.

On the other hand, hot matter galaxies follow a top to bottom sequence of formation. Observation from the remote galaxies suggests that the formation of matter occurs by “bottom-up” scenario. Thus, hot matter such as massive neutrino is not responsible for formation of galaxies and hence is not the dominant form of dark matter.

Conclusion:

From this observation, it is concluded that the prominent form of dark matter is cold. This suggests that massive neutrinos (which are hot) do not constitute prominent type of dark matter present in the universe.

Answer 6

Chapter 26, Problem 46Q

(a)

To determine

The mass of neutrinos in the unit of kilograms and also as a fraction of the mass of the electron, if the Hubble constant is about 73 km/s/Mpc, critical density ρc is 1×10−26 kg/m3 and its average density is about 0.20 ρc. The average density of a neutrino in space is about 100 neutrino/cm3.

(a)

Expert Solution

Answer to Problem 46Q

Solution:

2×10−35 kg, 2.1×10−5

Explanation of Solution

Given data:

The Hubble constant has a value of 73 km/s/Mpc.

The critical density has a value of 1×10−26 kg/m3.

The average density of dark matter is 0.20ρc.

The average density of neutrino throughout the space is 100 neutrino/cm3.

Formula used:

The relation between the Hubble law and critical density is presented below.

ρc= 3H028πG

In the equation, G is the universal constant whose value is 6.67×10−11 N⋅m2/kg, H0 is the Hubble constant and ρc is the critical density.

Explanation:

Convert the value of H0 into seconds.

H0= 73 km/s/Mpc=73 kms⋅Mpc(1 Mpc3.08×1019 km)= 2.37×10−18 s−1

Recall, the expression for critical density.

ρc= 3H028πG

Substitute 2.37×10−18 s−1 for H0 and 6.67×10−11 N⋅m2/kg for G.

ρc= 3(2.37×10−18 s−1)2 8π(6.67×10−11 N⋅m2/kg)=1×10−26 kg/m3

Average density of dark matter is 0.20ρc.

ρdm=0.20ρc

In the relation above, ρdm is the average density of dark matter.

Substitute 1×10−26 kg/m3 for ρc.

ρdm= 0.20(1×10−26 kg/m3)= 2×10−27 kg/m3

The average density of neutrino throughout the space is 100 neutrino/cm3. So, the number of the neutrino in a cubic meter of space is obtained as follows.

n=100 cm−3(106 cm31 m3)=108 m−3

Therefore, the mass of the neutrino is obtained from the following calculation.

m=ρdmn

Substitute 2×10−27 kg/m3 for ρdm and 108 m−3 for n.

m=2×10−27 kg/m3108 m−3=2×10−35 kg

The mass in terms of mass of electron (me) which has a value of 9.1×10−31 kg. Thus, the above value calculated in terms of electron mass as presented below.

m=2×10−35 kg(1 me9.1×10−31 kg)=2.2×10−5 me

Conclusion:

The mass of the neutrino in kilograms is 2×10−35 kg and as a fraction of mass of electron is 2.2×10−5.

Answer 7

Chapter 26, Problem 46Q

(a)

To determine

The mass of neutrinos in the unit of kilograms and also as a fraction of the mass of the electron, if the Hubble constant is about 73 km/s/Mpc, critical density ρc is 1×10−26 kg/m3 and its average density is about 0.20 ρc. The average density of a neutrino in space is about 100 neutrino/cm3.

Answer 8

(a)

Expert Solution

Answer to Problem 46Q

Solution:

2×10−35 kg, 2.1×10−5

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given data:

The Hubble constant has a value of 73 km/s/Mpc.

The critical density has a value of 1×10−26 kg/m3.

The average density of dark matter is 0.20ρc.

The average density of neutrino throughout the space is 100 neutrino/cm3.

Formula used:

The relation between the Hubble law and critical density is presented below.

ρc= 3H028πG

In the equation, G is the universal constant whose value is 6.67×10−11 N⋅m2/kg, H0 is the Hubble constant and ρc is the critical density.

Explanation:

Convert the value of H0 into seconds.

H0= 73 km/s/Mpc=73 kms⋅Mpc(1 Mpc3.08×1019 km)= 2.37×10−18 s−1

Recall, the expression for critical density.

ρc= 3H028πG

Substitute 2.37×10−18 s−1 for H0 and 6.67×10−11 N⋅m2/kg for G.

ρc= 3(2.37×10−18 s−1)2 8π(6.67×10−11 N⋅m2/kg)=1×10−26 kg/m3

Average density of dark matter is 0.20ρc.

ρdm=0.20ρc

In the relation above, ρdm is the average density of dark matter.

Substitute 1×10−26 kg/m3 for ρc.

ρdm= 0.20(1×10−26 kg/m3)= 2×10−27 kg/m3

The average density of neutrino throughout the space is 100 neutrino/cm3. So, the number of the neutrino in a cubic meter of space is obtained as follows.

n=100 cm−3(106 cm31 m3)=108 m−3

Therefore, the mass of the neutrino is obtained from the following calculation.

m=ρdmn

Substitute 2×10−27 kg/m3 for ρdm and 108 m−3 for n.

m=2×10−27 kg/m3108 m−3=2×10−35 kg

The mass in terms of mass of electron (me) which has a value of 9.1×10−31 kg. Thus, the above value calculated in terms of electron mass as presented below.

m=2×10−35 kg(1 me9.1×10−31 kg)=2.2×10−5 me

Conclusion:

The mass of the neutrino in kilograms is 2×10−35 kg and as a fraction of mass of electron is 2.2×10−5.

Answer 13

(b)

To determine

The reason due to which astronomers do not consider massive neutrinos as the prominent type of dark matter.

(b)

Expert Solution

Answer to Problem 46Q

Solution:

The cold matter is the dominant form of dark matter. This suggests that massive neutrinos, which are hot, are not the dominant type of dark matter in the universe.

Explanation of Solution

Introduction:

Dark matter: Dark matter does not emit electromagnetic radiations and thus cannot be detected directly. It constitutes 80% of the universe. It is thought to be non-baryonic in nature which means it is composed of some undiscovered subatomic particles.

Explanation:

Example of hot dark matters are Neutrinos because they comprise of lightweight particles which travel at high speed. Cold matter, on the other hand, comprises of massive particles at low speed.

Massless neutrinos, like photons, always travel at the speed of light. However, neutrinos possess a small mass and the gravitational pull on surrounding matter. This graviational pull could lead to the formation of galaxies.

In cold matter, the formation of the galaxy takes place from bottom to up means the intersection between filaments occurs. These filaments merge together into galaxies. These galaxies are converted into clusters of galaxies, after which they become superclusters.

On the other hand, hot matter galaxies follow a top to bottom sequence of formation. Observation from the remote galaxies suggests that the formation of matter occurs by “bottom-up” scenario. Thus, hot matter such as massive neutrino is not responsible for formation of galaxies and hence is not the dominant form of dark matter.

Conclusion:

From this observation, it is concluded that the prominent form of dark matter is cold. This suggests that massive neutrinos (which are hot) do not constitute prominent type of dark matter present in the universe.

Answer 14

(b)

To determine

The reason due to which astronomers do not consider massive neutrinos as the prominent type of dark matter.

Answer 15

(b)

Expert Solution

Answer to Problem 46Q

Solution:

The cold matter is the dominant form of dark matter. This suggests that massive neutrinos, which are hot, are not the dominant type of dark matter in the universe.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Introduction:

Dark matter: Dark matter does not emit electromagnetic radiations and thus cannot be detected directly. It constitutes 80% of the universe. It is thought to be non-baryonic in nature which means it is composed of some undiscovered subatomic particles.

Explanation:

Example of hot dark matters are Neutrinos because they comprise of lightweight particles which travel at high speed. Cold matter, on the other hand, comprises of massive particles at low speed.

Massless neutrinos, like photons, always travel at the speed of light. However, neutrinos possess a small mass and the gravitational pull on surrounding matter. This graviational pull could lead to the formation of galaxies.

In cold matter, the formation of the galaxy takes place from bottom to up means the intersection between filaments occurs. These filaments merge together into galaxies. These galaxies are converted into clusters of galaxies, after which they become superclusters.

On the other hand, hot matter galaxies follow a top to bottom sequence of formation. Observation from the remote galaxies suggests that the formation of matter occurs by “bottom-up” scenario. Thus, hot matter such as massive neutrino is not responsible for formation of galaxies and hence is not the dominant form of dark matter.

Conclusion:

From this observation, it is concluded that the prominent form of dark matter is cold. This suggests that massive neutrinos (which are hot) do not constitute prominent type of dark matter present in the universe.