Energy separation between two states?

In summary, the question involves calculating the energy separation between the 4s state and the ground state of an aluminum atom, given that the wavelength of radiation emitted when the outermost electron falls to the ground state is 395 nm. The attempted solution involves using the equation E = h * c / λ and possibly drawing an energy level diagram. The Rydberg equation is not applicable in this case.
  • #1
spaghettibretty
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Homework Statement



The wavelength of the radiation emitted when the outermost electron of Al (Aluminum) falls from the 4s state to the ground state is about 395 nm. Calculate the energy separation (in joules) between these two states in the Al atom. Draw an energy level diagram of the states and transitions discussed.

Homework Equations



The ground state electron configuration of Al is 1s22s22p63s23p1, if that helps.
In my attempted solution I also use E = h * c / λ.
Rydberg equation: E = -(2.18e-18 J) * (Z)2 * (1/n22 - 1/n12)

The Attempt at a Solution


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I'm not one hundred percent sure on what the question is asking. Would the outermost electron falling to the ground state mean it goes from 4s to 3p? In this case do I have to use the rydberg equation with the 2 n's being 3 and 4?
Or does that not matter and all I have to do is plug it into E = h * c / λ, where E is the energy separation between the 4s state and the ground state? I'm also suppose to draw an energy level-diagram, I know how to set it up and all that, but would the arrow go from 4s to 3p or would it go from 4s to the very bottom (the ground state)?
 
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  • #2
spaghettibretty said:
Would the outermost electron falling to the ground state mean it goes from 4s to 3p?
Correct.

spaghettibretty said:
In this case do I have to use the rydberg equation with the 2 n's being 3 and 4?
The Rydberg formula is only valid for one-electron atoms. (In some special cases, it can be adapted to some other atoms using quantum defect theory, but this is not relevant here.)

spaghettibretty said:
Or does that not matter and all I have to do is plug it into E = h * c / λ, where E is the energy separation between the 4s state and the ground state?
This.

spaghettibretty said:
I'm also suppose to draw an energy level-diagram, I know how to set it up and all that, but would the arrow go from 4s to 3p or would it go from 4s to the very bottom (the ground state)?
What do you think?
 

Related to Energy separation between two states?

1. What is the concept behind energy separation between two states?

The concept of energy separation between two states refers to the difference in energy levels between two distinct states of a system. This energy difference can be due to various factors such as changes in the electron configuration, molecular structure, or physical conditions of the system.

2. How is energy separation between two states measured?

The energy separation between two states is typically measured using spectroscopic techniques, such as absorption, emission, or nuclear magnetic resonance spectroscopy. These methods involve the absorption or emission of photons by the system, which can provide information about the energy levels and their separation.

3. What is the significance of energy separation between two states in chemistry?

In chemistry, energy separation between two states is crucial as it determines the reactivity and stability of a molecule. The energy difference between the ground state and excited state of a molecule can determine the rate of a chemical reaction and the stability of the molecule in different environments.

4. How does energy separation between two states affect electronic transitions?

The energy separation between two states plays a significant role in electronic transitions, which involve the movement of electrons from one energy level to another. The energy difference between the two states determines the energy of the absorbed or emitted photon during the transition, and therefore, the color of light observed.

5. Can the energy separation between two states be manipulated?

Yes, the energy separation between two states can be manipulated through various methods, such as changing the temperature, pressure, or chemical environment of the system. Additionally, external factors such as electromagnetic fields or light can also be used to alter the energy levels and their separation in a system.

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