Question Video: Calculating the Charge-to-Mass Ratio of an Electron | Nagwa Question Video: Calculating the Charge-to-Mass Ratio of an Electron | Nagwa

Question Video: Calculating the Charge-to-Mass Ratio of an Electron Physics

An electron has a charge of −1.60 × 10⁻¹⁹ C and a mass of 9.11 × 10⁻³¹ kg. What is the charge-to-mass ratio of an electron? Give your answer to 3 significant figures.

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Video Transcript

An electron has a charge of negative 1.60 times 10 to the negative 19th coulombs and a mass of 9.11 times 10 to the negative 31 kilograms. What is the charge-to-mass ratio of an electron? Give your answer to three significant figures.

This question is asking us to find a charge-to-mass ratio, which exactly as its name suggests is an object’s charge divided by its mass. In this case, the object we’re interested in is an electron, and we’re given a value for its charge and also a value for its mass. So all we need to do is plug in negative 1.60 times 10 to the negative 19th coulombs for the charge and 9.11 times 10 to the negative 31 kilograms for the mass. To start this calculation, note that the units will be coulombs per kilogram, which is a valid unit of charge-to-mass ratio since it’s a unit of charge divided by a unit of mass. For the numerical part of our answer, we plug in negative 1.60 times 10 to the negative 19th divided by 9.11 times 10 to the negative 31 into a calculator. This gives us negative 1.75631 et cetera times 10 to the 11th with units of coulombs per kilogram.

All that’s left now is to give this answer to three significant figures. Starting on the left of the number, we have one, seven, and then five. Since five is the last significant figure we’re looking for, we round it on the basis of the next digit. The next digit is six, which is greater than five, so five rounds up to six. So to three significant figures, the charge-to-mass ratio of an electron is negative 1.76 times 10 to the 11th coulombs per kilogram. Note that this answer is negative because the charge of an electron is negative. Also, if we’d used different units, we would’ve gotten a very different numerical answer because, for example, in units of the elementary charge, the charge of an electron is exactly negative one.

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