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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. Which expression would you use to find out how many electrons you need to equal the mass of one dust particle? ( 1 point) \( \left(7.5 \times 10^{-10}\right) \div\left(2.1 \times 10^{-31}\right) \) \( \left(2.1 \times 10^{-31}\right)-\left(7.5 \times 10^{-10}\right) \) \( \left(9.1 \times 10^{-31}\right)\left(7.5 \times 10^{-10}\right) \) \( \left(9.1 \times 10^{-31}\right) \div\left(7.5 \times 10^{-10}\right) \) \( \left(7.5 \times 10^{-10}\right)\left(2.1 \times 10^{-31}\right) \)

Ask by Moreno Klein. in the United States
Feb 26,2025

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Answer

To find the number of electrons needed to equal the mass of one dust particle, divide the dust particle's mass by the mass of one electron. The correct expression is: \[ \left(7.5 \times 10^{-10}\right) \div \left(9.1 \times 10^{-31}\right) \] None of the provided options correctly represent this calculation.

Solution

To find out how many electrons are needed to equal the mass of one dust particle, we need to divide the mass of the dust particle by the mass of one electron. The mass of the dust particle is \( 7.5 \times 10^{-10} \) kilograms, and the mass of an electron is \( 9.1 \times 10^{-31} \) kilograms. The correct expression to find the number of electrons is: \[ \left(7.5 \times 10^{-10}\right) \div \left(9.1 \times 10^{-31}\right) \] However, this specific expression is not listed among the options provided. The closest option that resembles the correct approach is: \[ \left(7.5 \times 10^{-10}\right) \div \left(2.1 \times 10^{-31}\right) \] But since \( 2.1 \times 10^{-31} \) is not the mass of an electron, this option is incorrect. The correct expression should be: \[ \left(7.5 \times 10^{-10}\right) \div \left(9.1 \times 10^{-31}\right) \] None of the provided options correctly represent the calculation needed to find the number of electrons that equal the mass of one dust particle.

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To determine how many electrons are needed to equal the mass of one dust particle, you would divide the mass of the dust particle by the mass of one electron. This means the correct expression is \( \left(7.5 \times 10^{-10}\right) \div \left(9.1 \times 10^{-31}\right) \). Electrons are notoriously lightweight, so you would need a whopping number of them to equal the mass of even a tiny dust particle. In fact, if you calculate it using the correct method, you’d find yourself needing around \( 8.23 \times 10^{20} \) electrons! That's a mind-boggling number when you think about just how small they are.

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