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For a hydrogen atom in its ground state, use the Bohr model to compute (a) the orbital speed of the electron, (b) the kinetic energy of the electron, and (c) the electrical potential energy of the atom.

a) $2.19 \times 10^{6} \mathrm{m} / \mathrm{s}$

b) 13.6 $\mathrm{eV}$

c) $-27.2 e V$

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Rutgers, The State University of New Jersey

Numerade Educator

Hope College

University of Sheffield

In this exercise, we have a hydrogen atom at its ground state. And in question eight, we have to find what is the orbit of speed of the electric. I mean, and for that I'm gonna use the fact that the angular momentum is given by N. H. Bar. So the angular momentum of the electricity is just a bar for an equals one. Since here we're working with, ah, the ground state. But also we have that the angular momentum is the linear momentum, which is envy times the radius R of the orbit. So we have that V. We can isolate being this equation and have the three equals. H bar divided by I m are where m is the mass of the election. Ah, and are the radius of the orbit is given by and square a zero, which in our case, is just a zero. That's the Bohr radius cape, because an equals one and this is equal to 5.29 times centered at minus 11 meters. So now we can substitute this into their former for V, so V equals age over two pi. That's a bar times a mess of the election times radios. So this is 6.63 times 10 to the minus 34 usual second, divided by two pi times the mass of the electron, which is 9.1 time sent to the minus 31 kilograms times the radius, which isn't 5.29 time since the miners. 11 meters. So the speed V is equal to 2.19 times 10 to the six meters per second. This here is the question. The answer to question a question be You have to calculate the kinetic energy of the electric. Okay, and the kinetic energy you is just m V square over to and is the mass of the electoral. So that's 9.1 times 10 to the minus 31 kilograms. V is two point 19 times 10 to the sixth meters per second and I have two squared. Oh, there's divided by two. So have a K is equal to 2.18 time step the minus 18 Jews. And what I'm gonna do is to divide this by 1.6 times 10. So the mind as 19th you'll spare election vote. You know, I'm just transforming units here concerning the Connecticut energy from modules so that I can vote and the result is 13.6. Annex invoked. Okay, in questions. See, we have to calculate the potential energy and the potential energy is equal to K columns. Constant times the charge of the electorate, which is mine. A z times the charge of the Prodan, which is blowzy. So there's any square here divided by R. So I'm going to separate this in minus K e over r All this multiplied by E. Let's just say that I'm gonna leave out one of the ease here because I wanna I want the results to pop out in election votes. So here I have minus nine times sin to the ninth Newtons meters squared. Put him square times the charge of the electorate, which is 1.6 time stand to the minus 19 Coombs divided by R and are the radius as we calculate it back in question A is to, uh, no, I'm sorrys. Exactly. Five 0.29 time. Stand to the minus 11 meters. Oh, this times a So what we have here is minus 27 went to votes times E. So it's minus 27.2 election votes. That's the energy, the potential energy between the protein on the election. This concludes the exercise.

Universidade de Sao Paulo