Mass of a typical star is 10^30 kg . Assume that star is 3/4 hydrogen and 1\4 helium by mass. The estimated number of protons (which are present in hydrogen and helium both) in a typical star is equal to -

To determine the estimated number of protons in a typical star with a mass of \(10^{30}\) kg, where the composition is 75% hydrogen and 25% helium by mass, we can break down the problem step by step.

Understanding the Composition

First, let's calculate the mass of hydrogen and helium in the star:

• Mass of hydrogen = \( \frac{3}{4} \times 10^{30} \, \text{kg} = 7.5 \times 10^{29} \, \text{kg}\)
• Mass of helium = \( \frac{1}{4} \times 10^{30} \, \text{kg} = 2.5 \times 10^{29} \, \text{kg}\)

Calculating the Number of Protons

Next, we need to find out how many protons are in each of these elements:

Hydrogen

Hydrogen has an atomic mass of approximately 1 atomic mass unit (amu), which is equivalent to about \(1.67 \times 10^{-27}\) kg per atom. Since each hydrogen atom contains one proton, we can calculate the number of hydrogen atoms (and thus protons) as follows:

Number of hydrogen atoms = \( \frac{\text{Mass of hydrogen}}{\text{Mass of one hydrogen atom}} = \frac{7.5 \times 10^{29} \, \text{kg}}{1.67 \times 10^{-27} \, \text{kg/atom}} \approx 4.49 \times 10^{56} \, \text{atoms}\)

Helium

Helium has an atomic mass of about 4 amu, which corresponds to approximately \(6.64 \times 10^{-27}\) kg per atom. Each helium atom contains two protons, so we calculate the number of helium atoms and then the total number of protons:

Number of helium atoms = \( \frac{\text{Mass of helium}}{\text{Mass of one helium atom}} = \frac{2.5 \times 10^{29} \, \text{kg}}{6.64 \times 10^{-27} \, \text{kg/atom}} \approx 3.77 \times 10^{55} \, \text{atoms}\)

Since each helium atom has two protons, the total number of protons from helium is:

Total protons from helium = \(2 \times 3.77 \times 10^{55} \approx 7.54 \times 10^{55} \, \text{protons}\)

Summing Up the Protons

Now, we can find the total number of protons in the star by adding the protons from hydrogen and helium:

Total number of protons = Protons from hydrogen + Protons from helium

Total number of protons = \(4.49 \times 10^{56} + 7.54 \times 10^{55} \approx 5.24 \times 10^{56} \, \text{protons}\)

Final Result

Therefore, the estimated number of protons in a typical star with a mass of \(10^{30}\) kg, composed of 75% hydrogen and 25% helium, is approximately \(5.24 \times 10^{56}\) protons. This immense number reflects the vast scale of stellar matter and the fundamental role that protons play in the structure of atoms and the universe itself.