Is Negative Energy Possible in the Bohr Model?

[asdf1]

in the bohr model, the electron is in constant motion. how can such an electron have a negative amount of energy?

p.s.
sorry for clogging up this area with so many questions... I've been having a hard time understanding this area~

 

[jtbell]

The potential energy (in this situation) is negative, and has a larger magnitude than the kinetic energy, which is positive. So the total energy is negative.

For mathematical convenience, we set the total energy to be zero when the electron and the proton are infinitely far apart, and at rest with respect to each other. In order to separate a hydrogen atom "completely" into this state, we have to do work on it (add energy to it). Therefore its initial energy must be negative, so that the final energy can end up as zero.

If we wanted to, we could set the ground state energy of hydrogen equal to zero. Then the "completely separated" state described above would have energy +13.6 eV. But some of our equations would become more complicated, as a result.

 

[Tide]

The electron's energy is made up of its kinetic energy and potential energy. Since the nucleus is positively charged the potential energy of the electron must decrease (charge times potential) as it gets closer to the nucleus in order for the force to be attractive. Generally, we choose the potential energy to be 0 at infinity making the potential energy negative at all finite distances. When the electron is bound to the nucleus the magnitude of the potential energy is greater than the kinetic energy.

Therefore, the total energy of the electron is negative.

 

[asdf1]

thank you very much! :)