Calculating the energy of a hydrogen atom

In summary, the problem involves a sample of hydrogen atoms in the n=5 state and finding the number of different photon energies emitted when they all return to the ground state. Using the equation E= hc/lambda =(E(initial) -E(final)), and the formula 1/lambda = R*(1/m^2-(1/n^2)), it is possible to find the energy of the hydrogen atom between transitions. However, it is unclear how to find the number of photon energies. One suggestion is to use combinations, specifically 5 choose 2.
  • #1
Benzoate
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Homework Statement



A sample of hydrogen atoms are all in the n=5 state. If all the atoms return to the ground state, how many different photon energies will be emitted , assuming all possible transitions occur?

Homework Equations


possible equation: E= hc/lambda =(E(initial) -E(final)) .
1/lambda = R*(1/m^2-(1/n^2))

The Attempt at a Solution



Not sure where to begin on this problem, but I suspect I should find the energy of the hydrogen atom between the transitons of the two state. I know n=1 for the ground state.

1/lambda=1.097*10^7*(1/1^2-(1/5^2))

Not sure how to find the Number of photon energies :(
 
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  • #2
why hasn't anyone answer my question
 
  • #3
Wouldn't you just have 1 possible transition for every 2 states... so using combinations wouldn't the answer be 5 choose 2?
 

1. How is the energy of a hydrogen atom calculated?

The energy of a hydrogen atom can be calculated using the equation E = -13.6/n^2, where E is the energy in electron volts (eV) and n is the principal quantum number.

2. What is the significance of the principal quantum number in calculating the energy of a hydrogen atom?

The principal quantum number, denoted as n, represents the energy level or shell of the electron in a hydrogen atom. As the value of n increases, the energy of the electron decreases and it is located further from the nucleus.

3. How does the energy of a hydrogen atom change with different values of the principal quantum number?

As the principal quantum number increases, the energy of a hydrogen atom decreases. This is because the electron is located further from the nucleus and experiences less attraction to the positively charged nucleus.

4. Can the energy of a hydrogen atom be negative?

Yes, the energy of a hydrogen atom can be negative. This indicates that the electron is in a bound state, meaning it is attracted to the nucleus and has a lower energy than if it were free.

5. Are there any other factors that can affect the energy of a hydrogen atom?

Yes, the energy of a hydrogen atom can also be affected by external influences such as electric and magnetic fields. These fields can alter the energy levels and cause transitions between them.

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