How Does the Mass of a Nucleus Compare to the Mass of the Electrons?

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The mass of a nucleus compares to the mass of electrons in a number of really interesting and important ways. Find out about how the mass of a nucleus compares to the mass of electrons with help from an applied physics professional in this free video clip.

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Hello, my name is Walter Unglaub, and this is "how does the mass of a nucleus compare to the mass of the electrons?" So, here I have a little diagram of an atom, with a nuclei, comprised of various nucleons. They can be protons and neutrons, and here, I have orbiting electrons. Now, we're going to consider the scenario, in which we have a neutral atom, meaning we have just as many electrons in the atom as we do protons in the nucleus, so that it's electrically neutral overall. And, I'm going to consider light nuclei, where we just have a handful of nucleons in the nucleus. So, if we're considering a light nucleus, then the ratio of neutrons to protons, N over Z, is usually, or typically equal to one. For much heavier elements, this ratio can go as high as one point six. So, in this case, we're going to assume that we have just as many neutrons as we do protons. Now, the next step is to understand what the mass is of a proton, a neutron, and an electron. Mass of a proton is approximately 938.272 mega electron volts, per speed of light, squared. Where, here, I'm using units of energy, of electron volts, for the rest mass of a proton, from the equation E equals MC squared. A neutron has a slightly larger mass, 939.565, MEV over speed of light squared. Finally, an electron is several orders of magnitude lighter. It's equal to approximately point five one one mega electron volts per speed of light, squared. So, the next thing that I'm going to do is if I assume that I have as many neutrons as protons, I'm just gonna take an average of these two masses. So, the average mass of a nucleon is going to be approximately 939 mega electron volts per speed of light, squared. So, now, I can answer the question, "what is the ratio of the mass of the nucleus to that of all the electrons in a light neutral atom?" So, I start with the number of neutrons times the mass of the neutron, plus the number of protons times the mass of the proton, divided by the number of electrons times the mass of the electron. So, again, I'm assuming I have just as many electrons as I do protons, which is why I use Z. Making this approximation, because these two masses are very similar, they're almost the same, compared to the mass, from the point of view of an electron, I have two times Z times the average mass of a neutron divided by Z mass of an electron. Z's cancel out, so I have two times 939 divided by point five one one, so this is approximately equal to 3,675.15. So, to answer the original question, we see that the mass of the nucleus compared to the mass of all the electrons, in a light neutral atom, is several thousands time, several thousand times greater than the mass of an electron. So, very large ratio. So, all, almost all of the mass of an atom is concentrated in the nucleus. My name is Walter Unglaub, and this is "how does the mass of a nucleus compare to the mass of the electrons?"

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