What is the formula for the width of the potential box?

The excited electron in the potential box has a quantum number of 4, which corresponds to an energy of -3.4 eV. When it de-excites to the ground state, it emits a photon with the same energy. This photon is then absorbed by the hydrogen atom's electron, causing it to jump from the ground state to an excited state with quantum number 3, corresponding to an energy of -1.51 eV. We can use the equation for energy levels in the hydrogen atom to calculate the energy of the photon absorbed, and then equate it to the energy of the emitted photon to solve for L. In summary, an excited electron in a 1D potential box de-excites to the ground state and emits a
  • #1
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Homework Statement


An excited electron (quantum number =4) in a 1D potential box de-excites to the ground state and emit a photon. This photon subsequently becomes absorbed by an electron in a hydrogen atom. The electron in the hydrogen atom becomes excited to an excited state with quantum number =3. The process is illustrated in the following diagram. Determine the width of the potential box L.


Homework Equations


n(subscript n)=-13.6/n^2 eV

or frequency= 3.29x10^15 x Z^2(1/nfinal-1/ninitial) then use E=hf. I actually don't really understand when to use which equation. Can someone kindly explain to me?

Also, what is the formula to calculate the width of the particle in box box?
Thank you very much!

The Attempt at a Solution

 
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  • #2
Think about the energies of the original electron, the photon it emits, and the hydrogen atom's electron.
 

What is the formula for the width of the potential box?

The formula for the width of the potential box is determined by the specific system and conditions of the box. However, a general formula for the width can be written as:
W = (2mE - 2mU₀L²)^1/2, where W is the width, m is the mass of the particle, E is the energy, U₀ is the potential energy, and L is the length of the box.

What factors influence the width of the potential box?

The width of the potential box is influenced by the mass of the particle, the energy of the particle, and the potential energy of the system. Additionally, the length of the box can also affect the width.

Can the formula for the width of the potential box be applied to all systems?

The general formula for the width of the potential box can be applied to most systems, but it may need to be modified for certain systems that have unique conditions or properties.

How does the width of the potential box affect the behavior of the particle?

The width of the potential box determines the allowed energy levels and states for the particle. A wider potential box will have more allowed energy levels and states, while a narrower box will have fewer. This can impact the behavior and movement of the particle within the box.

What happens if the width of the potential box is infinite?

If the width of the potential box is infinite, it essentially becomes a free particle with no restrictions on its movement. This means that the energy levels and states are continuous, and the particle can move freely within the system without being confined to specific energy levels or states.

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