Subjects physics

Proton Mass E18Ad1

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1. **State the problem:** We want to find the total mass of all the protons in Betelgeuse given the number of protons and the mass of one proton. 2. **Given:** - Number of protons: $2.16 \times 10^{58}$ - Mass of one proton: $1.67 \times 10^{-27}$ kg 3. **Formula:** Total mass $= \text{number of protons} \times \text{mass of one proton}$ 4. **Calculate:** $$ 2.16 \times 10^{58} \times 1.67 \times 10^{-27} = (2.16 \times 1.67) \times 10^{58 + (-27)} $$ 5. **Simplify the coefficients:** $$ 2.16 \times 1.67 = 3.6072 $$ 6. **Add the exponents:** $$ 58 + (-27) = 31 $$ 7. **Combine results:** $$ 3.6072 \times 10^{31} \text{ kg} $$ 8. **Interpretation:** The total mass of all the protons in Betelgeuse is approximately $3.6072 \times 10^{31}$ kilograms. 9. **Regarding the scientists' answers:** - The correct calculation is $2.16 \times 10^{58} \times 1.67 \times 10^{-27} = 3.6072 \times 10^{31}$. - The calculator screen showing $3.6072 \times 10^{85}$ is incorrect because it did not account for the negative exponent properly. - Adding the numbers in scientific notation as in $2.16e58 + 1.67e-27$ is not appropriate here since we are multiplying quantities. **Final answer:** $$ \boxed{3.6072 \times 10^{31} \text{ kg}} $$