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Concept explainers
To show: The Jeans length of the early universe was 100 ly and the total mass of the universe was
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Explanation of Solution
Given data:
Temperature of the early universe is
Formula used:
According to Jeans, an object will only grow if the fluctuation in density crosses the density that is called Jean Length. Jeans length is calculated by the expression.
Here, k is Boltzmann constant, T is the temperature, m is the mass of a single particle in the gas, G is the universal gravitational constant, and
The expression for mass is:
Here, m is the mass, V is the volume, and
The volume of a sphere is:
Here, r is the radius of the sphere.
The relation between light year and meter is:
The mass of the sun is denoted as:
Explanation:
Consider the value of Boltzmann constant, universal gravitational constant, and mass of hydrogen as
Recall the expression for calculating the Jean length.
Substitute
Since the length of the universe is given as 100 ly, convert the above Jeans length into ly by using the conversion formula.
Consider the sphere of diameter equal to Jean length. Recall the expression for volume.
Substitute
Recall the expression of mass.
Substitute
Conclusion:
Therefore, by substituting the condition prevalent in the early universe, it can be concluded that the Jeans length for the early universe is nearly 100 ly and the total mass nearly is
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Chapter 26 Solutions
Universe
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