Question Video: Using the Charge-to-Mass Ratio to Find the Mass of a Particle | Nagwa Question Video: Using the Charge-to-Mass Ratio to Find the Mass of a Particle | Nagwa

# Question Video: Using the Charge-to-Mass Ratio to Find the Mass of a Particle Physics

A new particle has been discovered with a charge of 3.2 × 10⁻¹⁹ C and a charge-to-mass ratio of 4.45 × 10⁷ C/kg. What is the mass of the particle? Give your answer to 3 significant figures.

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### Video Transcript

A new particle has been discovered with a charge of 3.2 times 10 to the negative 19th coulombs and a charge-to-mass ratio of 4.45 times 10 to the seventh coulombs per kilogram. What is the mass of the particle? Give your answer to three significant figures.

The question is asking us to find the mass of a particle given its charge and its charge-to-mass ratio. This is possible because the charge-to-mass ratio provides a relationship between an object’s charge and its mass. Specifically, the charge-to-mass ratio is a particle’s charge divided by its mass. If we plug in values from the question, we have 4.45 times 10 to the seventh coulombs per kilogram is equal to 3.2 times 10 to the negative 19th coulombs divided by the unknown mass. To solve for mass, we multiply both sides by mass and divide by 4.45 times 10 to the seventh coulombs per kilogram.

On the left-hand side, we have 4.45 times 10 to the seventh coulombs per kilogram in both the numerator and the denominator, so the division leaves us with just mass. On the right-hand side, mass in the numerator divided by mass in the denominator is just one, and we’re left with 3.2 times 10 to the negative 19th coulombs divided by 4.45 times 10 to the seventh coulombs per kilogram. All that’s left is to calculate. Let’s start off by dividing 3.2 times 10 to the negative 19th by 4.45 times 10 to the seventh. Plugging into a calculator gives us 7.19101 and several more decimal places times 10 to the negative 27th. As for the units, we have coulombs divided by coulombs per kilogram. Coulombs in the numerator divided by coulombs in the denominator is just one. And having per kilograms in the denominator is equivalent to having just kilograms in the numerator. So the overall units of our answer will be kilograms, which is good because we’re looking for a mass.

Now we just need to round our answer so it has three significant figures. The first three significant digits of our answer are seven, one, and nine. Looking at the next digit, one is less than five, so nine doesn’t change when we round to three significant figures. So to three significant figures, the mass of our particle is 7.19 times 10 to the negative 27th kilograms. As it happens, this mass that we’ve calculated and the provided charge match up very closely with the mass and charge of an 𝛼 particle.

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