# Question about the Bohr model of atom and and electron in an orbital

• I
• aaronll
In summary, when an electron gains energy, it gains potential energy and kinetic energy. Higher energy levels correspond to a greater expected value of r, and the electron doesn't become only "quicker" around the orbit.

#### aaronll

I have a question about what happen when an electron in the Bohr model of atom, gains energy because for example is "hitting" by a photon.
Electron have an energy, and it is the sum of potential and kinetic.
When they gain energy, they gain potential energy so they go further away from nucleus and become slower, or they gain kinetic energy so they become faster but near to nucleus? and why?
thanks

aaronll said:
I have a question about what happen when an electron in the Bohr model of atom, gains energy because for example is "hitting" by a photon.
Electron have an energy, and it is the sum of potential and kinetic.
When they gain energy, they gain potential energy so they go further away from nucleus and become slower, or they gain kinetic energy so they become faster but near to nucleus? and why?
thanks
In general, the greater the energy the further the electron is from the nucleus. This is true for QM atomic orbitals - and also true for classical orbits in an inverse square potential.

PeroK said:
In general, the greater the energy the further the electron is from the nucleus. This is true for QM atomic orbitals - and also true for classical orbits in an inverse square potential.
Thank you
But my question is because for an energy E i think there is ( if the orbit is circular with a definite radius r) an "infinite" amount of pairs of velocity and distance (v,r) with the same energy, so in what way when energy increase the electron be?
higher speed? higher potential?

aaronll said:
Thank you
But my question is because for an energy E i think there is ( if the orbit is circular with a definite radius r) an "infinite" amount of pairs of velocity and distance (v,r) with the same energy, so in what way when energy increase the electron be?
higher speed? higher potential?
Unlike the classical case, the orbitals are not well-defined trajectories. So, you have to calculate the expected values of ##r## and kinetic energy. These, however, follow the same principle that higher energy levels correspond to a greater expected value of ##r##.

It should be clear that if you give an electron too much energy then the atom is ionised and the electron is released - i.e. the energy takes it beyond any bound orbital.

PeroK said:
Unlike the classical case, the orbitals are not well-defined trajectories. So, you have to calculate the expected values of ##r## and kinetic energy. These, however, follow the same principle that higher energy levels correspond to a greater expected value of ##r##.

It should be clear that if you give an electron too much energy then the atom is ionised and the electron is released - i.e. the energy takes it beyond any bound orbital.
Maybe is the fact that higher energy levels correspond to a greater expected value of r, why the electron doesn't become only "quicker" around the orbit?

aaronll said:
Maybe is the fact that higher energy levels correspond to a greater expected value of r, why the electron doesn't become only "quicker" around the orbit?
... because the orbitals must satisfy the Schroedinger equation.

PeroK said:
... because the orbitals must satisfy the Schroedinger equation.
Ok... that is.
Thank you

Maybe it is interesting to first consider the classical case, e.g. a comet being hit by another one. This will primarily induce a change of the comets velocity including it's direction. If the comet was on a circular orbit before the collision, it will end up on an elliptical or even unbound hyperbolical orbit after the collision. On an elliptical orbit, both kinetic and potential energy will periodically change (anticyclically) between their maximum and minimum values.
By the virial theorem, however, their average values are always related as 2<T> = -<V>, at least for the bound elliptical orbits.
So besides a change in energy, there will in general be a change in angular momentum, which is also true in the atomic case.
The classical theory applies also to atoms if they are in highly excited states, so called Rydberg atoms.