If we assume the Sun is made totally out of hydrogen, how many hydrogen atoms are contained with the Sun? If the Sun converts half of these hydrogen atoms into helium over its lifetime of about ten billion years, how many hydrogen atoms are converted per second?
Mass of Sun = 1.989 x 10 to the 30 kg
Mass of Mh = 1.6735 x 10 to the -27 kg
Compute the number of moles of H atoms (or ions) by dividing the mass of the sun by 1.008 g/mole. Then multiply that by Avogadro's number, 6.02*10^23 particles/mole
(Hydrogen is not molecular or neutral atoms in the sun; it is ionized.)
Take half the number of H atoms and divide it by 10^9 years, converted to seconds, to answer the second question.
To calculate the number of hydrogen atoms contained in the Sun, we need to determine the total mass of hydrogen in the Sun and then convert it to the number of hydrogen atoms using the atomic mass of hydrogen.
1. Start by calculating the mass fraction of hydrogen in the Sun. We're assuming that the Sun is made entirely of hydrogen, so the mass fraction of hydrogen is 1.
Mass of hydrogen in the Sun = Mass of the Sun x Mass fraction of hydrogen
= 1.989 x 10^30 kg x 1
= 1.989 x 10^30 kg
2. Now, we will determine the number of moles of hydrogen in the Sun by dividing the mass of hydrogen by the molar mass of hydrogen.
Molar mass of hydrogen (Mh) = 1.6735 x 10^-27 kg
Number of moles of hydrogen = Mass of hydrogen / Molar mass of hydrogen
= 1.989 x 10^30 kg / 1.6735 x 10^-27 kg
= 1.189 x 10^57 moles
3. Finally, we will convert the number of moles of hydrogen to the number of hydrogen atoms using Avogadro's number, which is approximately 6.022 x 10^23 atoms/mol.
Number of hydrogen atoms = Number of moles of hydrogen x Avogadro's number
= 1.189 x 10^57 moles x 6.022 x 10^23 atoms/mol
= 7.158 x 10^79 atoms
Thus, assuming the Sun is made entirely of hydrogen, there are approximately 7.158 x 10^79 hydrogen atoms contained within it.
To calculate how many hydrogen atoms are converted per second over the Sun's lifetime, we need to determine the number of hydrogen atoms converted and divide it by the number of seconds in ten billion years.
Number of hydrogen atoms converted per second = Number of hydrogen atoms converted / Total time (in seconds)
4. The total time is given as ten billion years, which is equivalent to 10^10 years.
Total time (in seconds) = 10^10 years x 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute
Calculating this gives: Total time = 3.154 x 10^17 seconds
5. The number of hydrogen atoms converted is half of the total number of hydrogen atoms, which we calculated as 7.158 x 10^79 atoms.
Number of hydrogen atoms converted = 0.5 x 7.158 x 10^79 atoms
= 3.579 x 10^79 atoms
Finally, we can calculate the number of hydrogen atoms converted per second:
Number of hydrogen atoms converted per second = 3.579 x 10^79 atoms / 3.154 x 10^17 seconds
Simplifying this gives us:
Number of hydrogen atoms converted per second ≈ 1.135 x 10^62 atoms/second
Therefore, approximately 1.135 x 10^62 hydrogen atoms are converted into helium per second during the Sun's lifetime.