Mass of the Sun = 1.989 x 10^30 kg
Mass of Hydrogen Atom = 1.00794 grams
If we assume the Sun is made totally of hydrogen, how many hydrogen atoms are contained within the Sun? If the Sun converts hald of these hydrogen atoms into helium over its lifetime of about ten billion years, how many hydrogen atoms are converted per second?
1.989*10^30 /(1.00794*10^-3)
= 1.973 * 10^33
half converted = .9867*10^33 converted
ten billion = 10^10 years
10^10y * 365d/y *24h/d*3600s/h = 3.154*10^17 seconds
so
.9867*10^33 converted/3.154*10^17 seconds
= .3128*10^16
= 3.128 * 10^15
To find the number of hydrogen atoms in the Sun, we can calculate the total mass of the Sun and then convert it to the number of hydrogen atoms using the molar mass of hydrogen.
The mass of the Sun is given as 1.989 x 10^30 kg, and the mass of a hydrogen atom is given as 1.00794 grams. To convert the mass of the Sun from kg to grams, we multiply it by 1000 (since there are 1000 grams in a kilogram):
Mass of the Sun = 1.989 x 10^30 kg x 1000 = 1.989 x 10^33 grams
Next, we can calculate the number of moles of hydrogen in the Sun by dividing the mass of the Sun by the molar mass of hydrogen:
Number of moles of hydrogen = Mass of the Sun / Molar mass of hydrogen
The molar mass of hydrogen is approximately 1.00794 grams/mole, so:
Number of moles of hydrogen = 1.989 x 10^33 grams / 1.00794 grams/mole
Using this value, we can calculate the Avogadro's number, which gives the number of atoms in one mole:
Avogadro's number = 6.022 x 10^23 atoms/mole
Finally, we can calculate the number of hydrogen atoms in the Sun by multiplying the number of moles of hydrogen by Avogadro's number:
Number of hydrogen atoms = Number of moles of hydrogen x Avogadro's number
Now, let's do the calculations:
Number of moles of hydrogen = 1.989 x 10^33 grams / 1.00794 grams/mole
Number of moles of hydrogen = 1.973 x 10^33 moles
Number of hydrogen atoms = 1.973 x 10^33 moles x 6.022 x 10^23 atoms/mole
Number of hydrogen atoms = 1.187 x 10^57 atoms
Therefore, the number of hydrogen atoms in the Sun is approximately 1.187 x 10^57 atoms.
Now let's calculate how many hydrogen atoms are converted into helium per second over the Sun's lifetime of ten billion years.
First, we need to find the total number of hydrogen atoms that are converted into helium over ten billion years. To do this, we multiply the number of hydrogen atoms in the Sun by 0.5 (since half of them are converted):
Number of hydrogen atoms converted = 1.187 x 10^57 atoms x 0.5
Number of hydrogen atoms converted = 5.935 x 10^56 atoms
Next, we need to convert the length of ten billion years to seconds. There are 365 days in a year, 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute:
Number of seconds in ten billion years = 10,000,000,000 years x 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute
Now, let's do the calculations:
Number of seconds in ten billion years = 3,153,600,000,000 seconds
Finally, we can calculate the number of hydrogen atoms converted per second by dividing the number of hydrogen atoms converted by the number of seconds:
Number of hydrogen atoms converted per second = 5.935 x 10^56 atoms / 3,153,600,000,000 seconds
Therefore, the number of hydrogen atoms converted into helium per second over the Sun's lifetime of ten billion years is approximately 1.882 x 10^46 atoms.