(a)
The temperature required for the collision of two protons if
(a)
Answer to Problem 10.4P
The temperature required for the collision of two protons is
Explanation of Solution
Write the expression for the reduced mass of a proton-proton collision by equating kinetic energy to thermal energy.
Here,
Conclusion:
Assume that nuclei having velocities ten times the root-mean square value for the Maxwell-Boltzmann distribution can overcome the Coulomb barrier. Therefore,
Here, the separation between the charges to be
Substitute
Thus, the temperature required for the collision of two protons is
(b)
The ratio of the number of protons having velocities ten times the rms value to those moving at the rms velocity.
(b)
Answer to Problem 10.4P
The ratio of the number of protons having velocities ten times the rms value to those moving at the rms velocity is
Explanation of Solution
Write the expression for ratio of atoms having velocities equal to ten times the rms value to those having the rms value.
Here,
Conclusion:
On solving equation (2)
Thus,the ratio of the number of protons having velocities ten times the rms value to those moving at the rms velocity is
(c)
The number of hydrogen nuclei in the sun.
(c)
Answer to Problem 10.4P
The number of hydrogen nuclei in the sun is
Explanation of Solution
Write the expression for number of atomic nuclei in the sun.
Here,
Conclusion:
Substitute
Thus,the number of hydrogen nuclei in the sun is
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Chapter 10 Solutions
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