Question
The mass of a dust particle is approximately \( 7.5 \times 10^{-10} \) kilograms and the mass of an electron is \( 9.1 \times 10^{-31} \) kilograms. How many electrons does it take to equal the mass of a dust particle? (1 point) \( 8.2 \times 10^{20} \) \( 6.8 \times 10^{-40} \) \( 1.2 \times 10^{21} \) \( 8.2 \times 10^{-90} \) \( 1.2 \times 10^{-21} \) \( 6.8 \times 10^{-41} \)
Ask by Sandoval Campbell. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
It takes \( 8.2 \times 10^{20} \) electrons to equal the mass of a dust particle.
Solution
To find out how many electrons it takes to equal the mass of a dust particle, we need to divide the mass of the dust particle by the mass of an electron.
Given:
- Mass of a dust particle = \( 7.5 \times 10^{-10} \) kilograms
- Mass of an electron = \( 9.1 \times 10^{-31} \) kilograms
Let's calculate the number of electrons needed to equal the mass of a dust particle:
\[ \text{Number of electrons} = \frac{\text{Mass of dust particle}}{\text{Mass of an electron}} \]
\[ \text{Number of electrons} = \frac{7.5 \times 10^{-10}}{9.1 \times 10^{-31}} \]
\[ \text{Number of electrons} = 8.2 \times 10^{20} \]
Therefore, it takes \( 8.2 \times 10^{20} \) electrons to equal the mass of a dust particle.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Mind Expander
To find how many electrons it takes to equal the mass of a dust particle, we can use the formula: \[ \text{Number of electrons} = \frac{\text{Mass of dust particle}}{\text{Mass of one electron}} = \frac{7.5 \times 10^{-10} \text{ kg}}{9.1 \times 10^{-31} \text{ kg}} \] Now calculating that gives us: \[ \frac{7.5 \times 10^{-10}}{9.1 \times 10^{-31}} \approx 8.24 \times 10^{20} \] Rounding gives \( 8.2 \times 10^{20} \). So, the correct answer is \( \mathbf{8.2 \times 10^{20}} \). Let me know if you have more questions!