Question

the mass of a helium-4 atom is 6, point, 6, 5, times, 10, to the power minus 246.65×10 −24 grams. the mass of an electron is 9, point, 1, 1, times, 10, to the power minus 289.11×10 −28 grams. how many times greater is the mass of a helium-4 atom than the mass of an electron? write your answer in standard notation, rounding to the nearest tenth.

Answer 1

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.

1. **Mass of Helium-4 Atom**:
- Given: \( 6.65 \times 10^{-24} \) grams

2. **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:

1. **Divide the coefficients**:
\[
\frac{6.65}{9.11} \approx 0.729
\]

2. **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.