An a particle, 4He2 + , has a mass of 4.00151 amu. Find the value of its charge-to-mass ratio in C/kg.

Question

Accepted Answer

hey everyone in this example, we need to find the charge to mass ratio in columns per kilogram of the given alpha particle of helium. So we have helium with the mass, number four in the left hand exponents It's a 2-plus cat eye on and we are given the mass of 4.1 51 AM use. So we want to recall that one a.m. U. Is equal to a value of 1.66054 times 10 to the negative 27 power kilograms. So we're going to keep this conversion factor in mind so that we can convert from the given mass 4.1 51 AM us and turn that two kg. So we're going to multiply by the conversion factor. We're in our denominator. We should have one a.m. you And then in our numerator we'll have 1.66054 times 10 to the negative 27th power kg. So am us are aligned properly and we can cancel them out. Leaving us with kg until that gives us 6.6446, 7 Times 10 to the -27 Power kg. So now that we have our mass of helium in the proper units kilograms, we need to make sure that it's in columns per kilograms now. So we're going to recall the experiment which is the Malik in oil drop test and we want to recall that this oil drop test or this experiment determines Charges of electrons. So the charges of one electron. And so we want to recall that in our universe. The electron charge is equal to a value of 1. times 10 to the negative 19th power columns. And so we want to find helium on the periodic table. And we see that helium corresponds to atomic number two. So we recall that you should write the atomic number in the left hand subscript. So we have the two plus helium cat ion with atomic number two. And we want to recall that, that atomic number corresponds to two protons and two electrons in a neutral atom of helium. So if we didn't have this too plus charge here, This atomic # two would translate to us having two protons and two electrons. So what we would interpret that as is two times the given charge value for an electron in our universe. So two times 1.60 times 10 to the negative 19th power columns. And so this equals a value of three negative 3.2 times 10 to the negative 19th power columns. And so this is going to be our combined charge of the two Adams. Or sorry, the two electrons that would have been present if we were still a neutral atom of helium. But in this case we lost those two electrons. So this is the combined charge of those two lost electrons because we recall that acadian means we lose those electrons based on that charge. And so ultimately, now that we have this column value, we're going to get columns per kilograms by dividing these two values from one another for our final answer. So what we should have for columns per kilogram is one point three or sorry, the absolute value of 3.2 times 10 to the negative 19th power columns, Divided by the absolute value of 6.644, 6, 7 times 10 to the -27 power kg. And we want to take the absolute values because we want our units to be positive. We don't want anything to be negative here. And so what this is going to give us is a value of 4.82 times to the seventh power columns per kilogram or charges per kilogram. And so this completes this example as our final answer for the charge to mass ratio of the alpha particle of helium four. So if you have any questions, please leave them down below, but I hope I was able to help you understand. And I will see everyone in the next practice video

An a particle, 4He2 + , has a mass of 4.00151 amu. Find the value of its charge-to-mass ratio in C/kg.

Verified Solution

Key Concepts

Charge-to-Mass Ratio

Units of Measurement

Helium Ion (4He2+)