The mass of a dust particle is approximately 7.5×10−10

Question

kilograms and the mass of an electron is 9.1×10−31
kilograms. How many electrons does it take to equal the mass of a dust particle?(1 point)
Responses

6.8×10−41
6 point 8 times 10 to the negative 41 power

6.8×10−40
6 point 8 times 10 to the negative 40 power

8.2×10−20
8 point 2 times 10 to the negative 20 power

1.2×10−21
1 point 2 times 10 to the negative 21 power

1.2×1021
1 point 2 times 10 to the 21th power

8.2×1020

Answer 1

To find the number of electrons needed to equal the mass of a dust particle, you can divide the mass of the dust particle by the mass of a single electron.

Mass of the dust particle = \( 7.5 \times 10^{-10} \) kg
Mass of an electron = \( 9.1 \times 10^{-31} \) kg

Now let's calculate the number of electrons:

\[ \text{Number of electrons} = \frac{\text{Mass of dust particle}}{\text{Mass of an electron}} = \frac{7.5 \times 10^{-10} , \text{kg}}{9.1 \times 10^{-31} , \text{kg}} \]

Calculating the above expression:

\[ \text{Number of electrons} \approx \frac{7.5}{9.1} \times \frac{10^{-10}}{10^{-31}} = 0.826 \times 10^{21} \]

Now convert \( 0.826 \) to scientific notation: \[ 0.826 = 8.26 \times 10^{-1} \]

Thus:

\[ \text{Number of electrons} \approx 8.26 \times 10^{20} \]

Rounding to two significant figures, we get approximately:

\[ 8.2 \times 10^{20} \]

So, the answer is:

8.2 × 10²⁰ (which corresponds with the choice: 8.2×10²⁰).