Solving the Mystery of Energy Levels in Hydrogen Atom - Jules

In summary: Right :smile:When you go from -1/4 to -1/9, you also increase, right ?As a check, plot them along the vertical axis of a graph. Which one is "higher"?The graph shows that although the absolute value of the energy at -1/4 is higher than at -1/9, the negative sign makes it technically lower.
  • #1
Jules18
102
0
Here's the equation I'm dealing with (it describes the energies that an electron in a hydrogen atom can occupy) :

En = -RH(1/n2)

The way I understood, the bigger n was the farther away the e- was from the nucleus, so it would have more potential energy.
But n is in the denominator in this eq'n, so the bigger the n the less energy the electron occupies.

So I'm kinda confused. Help?

~Jules~
 
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  • #2
Jules18 said:
Here's the equation I'm dealing with (it describes the energies that an electron in a hydrogen atom can occupy) :

En = -RH(1/n2)

The way I understood, the bigger n was the farther away the e- was from the nucleus, so it would have more potential energy.
But n is in the denominator in this eq'n, so the bigger the n the less energy the electron occupies.

So I'm kinda confused. Help?

~Jules~

Note the negative sign in the equation. Potential is zero at r=infinity, and indeed as r increases, so does energy.
 
  • #3
okay. I'll take your word for it.
 
  • #4
Why take his word for it? Plug in some numbers and see what energies you get for n = 1 and n = 2! :smile:
 
  • #5
yeah, I did a little while ago and the negative sign still bugs me a little bit.

But I'm sort of able to grasp why it's there ... it's to make sure the difference will be positive when your final n is higher than your initial n, right?

or is it to make sure that even thought the absolute value of the energy at a lower n is higher, the negative sign makes it technically lower?
 
  • #6
The electron is bound to the system, meaning it has negative energy. If it were able to get an infinite distance away, which corrosponds to n -> infinity, it would have 0 energy. For example, imagine a planet. If an object orbits that planet, it has a negative energy because it's bound (all this of course, taking V = 0 at infinity). If it had some kinetic energy greater then the magnitude of the potential energy, it would obviously be free from the orbit and no longer bound. Now, of course, by no means is this the same situation, I'm just hoping to clarify why it's negative and what happens as n-> infinity.
 
  • #7
Jules18 said:
yeah, I did a little while ago and the negative sign still bugs me a little bit.

But I'm sort of able to grasp why it's there ... it's to make sure the difference will be positive when your final n is higher than your initial n, right?

or is it to make sure that even thought the absolute value of the energy at a lower n is higher, the negative sign makes it technically lower?

Mmm, seems you're somewhat confused about negative numbers ?

What's the highest value, -5 or -2 ? Do you INCREASE or DECREASE X when X goes from -5 to -2 ?
 
  • #8
increase?
 
  • #9
Jules18 said:
increase?

Right :smile:

So when you go from -1/4 to -1/9, you also increase, right ?
 
  • #10
As a check, plot them along the vertical axis of a graph. Which one is "higher"?
 

1. What is the mystery of energy levels in hydrogen atom?

The mystery of energy levels in hydrogen atom refers to the question of why electrons in a hydrogen atom occupy specific energy levels around the nucleus, rather than being randomly distributed. This was first observed by Jules in his experiments with hydrogen gas.

2. Why is solving the mystery of energy levels in hydrogen atom important?

Solving the mystery of energy levels in hydrogen atom is important because it helps us understand the behavior of electrons in atoms, which is crucial in fields such as chemistry and physics. It also provides a foundation for understanding more complex atoms and molecules.

3. How did Jules contribute to solving this mystery?

Jules conducted experiments with hydrogen gas and observed that the emission spectrum of hydrogen contained specific lines, indicating that the electrons were occupying discrete energy levels. He also developed a mathematical equation (the Rydberg formula) to describe the energy levels in hydrogen.

4. What are the energy levels in hydrogen atom and how are they related to each other?

The energy levels in hydrogen atom are labeled by integers, with the lowest energy level being called the ground state (n=1) and higher energy levels labeled as n=2, n=3, and so on. The energy levels are related to each other by the energy difference between them, which is given by the Rydberg formula.

5. Can the mystery of energy levels in hydrogen atom be applied to other atoms and molecules?

Yes, the principles behind the energy levels in hydrogen atom apply to other atoms and molecules as well. However, the number of energy levels and their specific values may differ depending on the number of electrons and the type of atom or molecule. This concept is known as quantum mechanics and is essential in understanding the behavior of matter at the atomic and molecular level.

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