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

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

8.2×1020
8 point 2 times 10 to the 20th power

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

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

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

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

Answer 1

To find out how many electrons are needed to equal the mass of a dust particle, we can use the formula:

\[ \text{Number of electrons} = \frac{\text{Mass of dust particle}}{\text{Mass of one electron}} \]

Given:

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

Now we can calculate the number of electrons:

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

Calculating this:

1. Calculate the division of the numbers:

\[ \frac{7.5}{9.1} \approx 0.8241758 \]

2. Calculate the powers of ten:

\[ 10^{-10} / 10^{-31} = 10^{-10 + 31} = 10^{21} \]

3. Combine the results:

\[ 0.8241758 \times 10^{21} \approx 8.24 \times 10^{20} \]

Thus, the number of electrons needed to equal the mass of a dust particle is approximately:

\[ 8.24 \times 10^{20} \]

From the provided options, the closest one is:

8.2×10²⁰

So, the answer is 8.2×10²⁰.