To compare the masses of a helium-4 atom and an electron, we first need to express both masses in scientific notation correctly and then divide them.
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Mass of Helium-4 Atom:
- Given: \( 6.65 \times 10^{-24} \) grams
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Mass of Electron:
- Given: \( 9.11 \times 10^{-28} \) grams
Now, to find out how many times greater the mass of the helium-4 atom is than the mass of the electron, we can set up the following division:
\[ \text{Ratio} = \frac{\text{Mass of Helium-4}}{\text{Mass of Electron}} = \frac{6.65 \times 10^{-24}}{9.11 \times 10^{-28}} \]
To simplify the calculation, we can divide the coefficients and subtract the exponents:
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Divide the coefficients: \[ \frac{6.65}{9.11} \approx 0.729 \]
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Subtract the exponents (when dividing exponents in scientific notation): \[ -24 - (-28) = -24 + 28 = 4 \]
So now we can express the result: \[ \text{Ratio} \approx 0.729 \times 10^{4} \]
Convert this into standard notation: \[ 0.729 \times 10^{4} = 7290 \]
Finally, rounding to the nearest tenth, we have: \[ \boxed{7290.0} \]
Thus, the mass of a helium-4 atom is approximately 7290.0 times greater than the mass of an electron.
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