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## AP®︎/College Physics 2

### Course: AP®︎/College Physics 2>Unit 8

Lesson 2: Atoms and electrons

# Bohr model energy levels (derivation using physics)

Using classical physics to calculate the energy of electrons in Bohr model. Solving for energy of ground state and more generally for level n.

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Created by Jay.

## Want to join the conversation?

• How can potential energy be negative? Wouldn't that be like saying you mass is negative?
Potential energy is energy stored in an object. Either you store energy ( +ve ) or not at all ( 0 ).
So why is it negative?
Also i heard that gravitational potential energy is negative . How can 'mgh' be -ve ?
A google search told me that 0 reference point is infinity. What does that mean why is it like that?
• In mgh h is distance relative to the earth surface. So if you lower than the earth's surface the potential eergy is negative
• Why do we write a single "r" in the formula of P.E? I understand how the single "r" came in the formula of kinetic energy but why do we use a single "r" in Potential energy formula?
• Hi, nice question.
The thing is that here we use the formula for electric potential energy, i.e. the energy associated with charges in a defined system. The Formula for electric potenial = (q)(phi)(r) = (KqQ)/r.
We use (KqQ)/r^2 when we calculate force between two charges separated by distance r. This is also known as ESF.
Due to the similarity, many people (wrongly) apply the ESF for potential energy
• so this formula will only work for hydrogen only right?!
and what happens if there are more than just one electron in an energy level?
• Yes. This formula will work for hydrogen and other unielecton ions like He+, Li^2+, etc.
When there are more than one electrons, then there is repulsion between those electrons due to their same negative charge. The formula then breaks down. Also note, the Bohr model is not what actually happens. The current quantum model is believed to be the most correct.
• What is quantized energy level?
Thanks.
• For energy to be quantized means that is only comes in discreet amounts. It is like if I need to give you some money, I can give you 1 cent or 10 cents but I can't give you 1/2 a cent because there are no 1/2 cent coins.
• The energy of these electrons is calculated as though they are in a circular orbit around the nucleus. But they're not in orbit around the nucleus. So why does this work?
• It doesn't work. That's why the Bohr model has been replaced by the modern model of the atom. The Bohr model only worked for Hydrogen atoms, and even for hydrogen it left a lot unexplained.
The reason it works somewhat for hydrogen is that even though the electrons are not in orbits there are certain energy concepts for orbits that have more universal applicability.
• What does Planck's constant represent?
• It tells about the energy of the frequency...... ...... Whose ratio is the Planck's constant
• Is this the same as -1/n2X13.6 eV
(1 vote)
• Yes, it is. Chemists tend to use joules an their energy unit, while physicists often use electron volts.
The formulas are the same. They are just using different units for the constant,
• Why do we take the absolute value for the kinetic energy but not for the potential energy? This matter is giving me all sorts of trouble understanding it deeply :(