Mass of a typical star is `1.0xx10^(30) kg`. Assume that a star is typically `3//4` hydrogen and `1//4` helium by mass. The estimated number of protons (which are present in H as well as He) in a typical star is approximately

Answer

To find the estimated number of protons in a typical star with a mass of \(1.0 \times 10^{30}\) kg, which is composed of \( \frac{3}{4} \) hydrogen and \( \frac{1}{4} \) helium by mass, we can follow these steps:

### Step 1: Determine the mass of hydrogen and helium in the star.
Given that the star's total mass is \(1.0 \times 10^{30}\) kg:
- Mass of hydrogen:
\[ \text{Mass of H} = \frac{3}{4} \times (1.0 \times 10^{30} \text{ kg}) = 0.75 \times (1.0 \times 10^{30} \text{ kg}) = 7.5 \times 10^{29} \text{ kg} \]
- Mass of helium:
\[ \text{Mass of He} = \frac{1}{4} \times (1.0 \times 10^{30} \text{ kg}) = 0.25 \times (1.0 \times 10^{30} \text{ kg}) = 2.5 \times 10^{29} \text{ kg} \]

### Step 2: Convert the masses to grams.
1 kg = 1000 grams, so:
- Mass of hydrogen in grams:
\[ \text{Mass of H} = 7.5 \times 10^{29} \text{ kg} \times 1000 \text{ g/kg} = 7.5 \times 10^{32} \text{ g} \]
- Mass of helium in grams:
\[ \text{Mass of He} = 2.5 \times 10^{29} \text{ kg} \times 1000 \text{ g/kg} = 2.5 \times 10^{32} \text{ g} \]

### Step 3: Calculate the number of moles of hydrogen and helium.
Using the molar mass:
- Molar mass of hydrogen (H) = 1 g/mol
- Molar mass of helium (He) = 4 g/mol

- Number of moles of hydrogen:
\[ n_H = \frac{7.5 \times 10^{32} \text{ g}}{1 \text{ g/mol}} = 7.5 \times 10^{32} \text{ mol} \]
- Number of moles of helium:
\[ n_{He} = \frac{2.5 \times 10^{32} \text{ g}}{4 \text{ g/mol}} = 0.625 \times 10^{32} \text{ mol} \]

### Step 4: Calculate the number of protons from hydrogen and helium.
- Each hydrogen atom has 1 proton, so:
\[ \text{Number of protons from H} = n_H \times N_A = 7.5 \times 10^{32} \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 4.51 \times 10^{56} \text{ protons} \]
- Each helium atom has 2 protons, so:
\[ \text{Number of protons from He} = 2 \times n_{He} \times N_A = 2 \times 0.625 \times 10^{32} \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 7.53 \times 10^{55} \text{ protons} \]

### Step 5: Calculate the total number of protons.
\[ \text{Total number of protons} = \text{Number of protons from H} + \text{Number of protons from He} \]
\[ \text{Total number of protons} \approx 4.51 \times 10^{56} + 7.53 \times 10^{55} \approx 5.26 \times 10^{56} \]

### Final Answer:
The estimated number of protons in a typical star is approximately \(5.26 \times 10^{56}\).

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