Which Bohr orbit does the electron occupy in this atom?

[map7s]

Homework Statement

he potential energy of a hydrogen atom in a particular Bohr orbit is -2.72 10-19 J.
(a) Which Bohr orbit does the electron occupy in this atom?
(b) Suppose the electron moves away from the nucleus to the next higher Bohr orbit. Does the potential energy of the atom increase, decrease, or stay the same?
(c) Calculate the potential energy of the atom for the orbit referred to in part (b).

Homework Equations

U=-ke^2/r
r=n^2 r
U=-ke^2/(n^2 r)

The Attempt at a Solution

I tried plugging in my numbers into the first equation and solving for r, but I got a really weird number with a very large negative exponent. I then tried plugging the numbers into the third equation (which is just a combination of the first two equations), and I got another really weird number. Am I not supposed to be using these equations?

 

[Astronuc]

Take a look at this and see if something comes to mind.

http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html#c4

 

[m2003]

I would approach this problem by first understanding the concept of Bohr orbits and their relationship to the potential energy of an atom. Bohr orbits are the specific energy levels that an electron can occupy in an atom, and each orbit has a specific potential energy associated with it. The potential energy of an electron in a hydrogen atom can be calculated using the equation U=-ke^2/(n^2 r), where k is the Coulomb constant, e is the charge of an electron, and r is the distance between the electron and the nucleus.

In this case, the potential energy is given as -2.72 x 10^-19 J, which means that the electron is in the first Bohr orbit (n=1), as this is the only orbit with a negative potential energy. Plugging this value into the equation, we can solve for r and find that the distance between the electron and the nucleus is approximately 5.3 x 10^-11 meters.

Moving on to part (b), we can see that the electron is now moving to the next higher Bohr orbit. As the electron moves further away from the nucleus, the distance (r) increases, and therefore the potential energy decreases. This is because the attractive force between the positively charged nucleus and the negatively charged electron decreases with increasing distance.

To calculate the potential energy for the next higher orbit, we can simply plug in the new value of n (n=2) into the equation and solve for U. This gives us a potential energy of -6.80 x 10^-20 J, which is a lower value than the previous orbit, indicating a decrease in potential energy.

Overall, as a scientist, I would use the given equations and concepts to accurately solve this problem and understand the relationship between Bohr orbits and potential energy in an atom.