How Many Spectral Lines are Produced During Electron Transitions in Hydrogen?

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SUMMARY

The discussion centers on the calculation of spectral lines produced during electron transitions in hydrogen. The formula for determining the number of spectral lines is given by {(n1-n2)(n1-n2+1)}/2, where n1 and n2 are the principal quantum numbers of the initial and final energy levels. A participant initially miscalculated the number of transitions when an electron jumps from the 4th shell (n=4) to the 2nd shell (n=2), overlooking the transition from the 3rd shell (n=3) to the 2nd shell. The correct number of spectral lines is indeed three, confirming the validity of the formula.

PREREQUISITES
  • Understanding of quantum mechanics and energy levels in atoms
  • Familiarity with the hydrogen atom's electron transitions
  • Knowledge of the principal quantum number (n) concept
  • Basic grasp of spectral lines and their significance in spectroscopy
NEXT STEPS
  • Study the derivation and application of the formula {(n1-n2)(n1-n2+1)}/2 for spectral lines
  • Explore the concept of electron transitions in multi-electron atoms
  • Learn about the Balmer series and its relation to hydrogen spectral lines
  • Investigate the role of energy levels in atomic spectroscopy
USEFUL FOR

Students of physics, educators teaching quantum mechanics, and anyone interested in atomic structure and spectroscopy will benefit from this discussion.

vkash
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no of line in line spectrum is equal to jumps of electron from one shell to another. Am i correct.

IN my book it is written that if a electron in hydrogen jumps from n1 to n2 then number of spectral lines is given by formula {(n1-n2)(n1-n2+1}/2. so consider a electron jump from 4th shell to 2nd shell then number of kinds of jump can be (1) 4th to 3rd,(2) 4th to 2nd So there are only two jumps. but if we apply formula then it will come out to be 3. So where i or formula is wrong.
thanks for any kind of help.
 
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vkash said:
no of line in line spectrum is equal to jumps of electron from one shell to another. Am i correct.

IN my book it is written that if a electron in hydrogen jumps from n1 to n2 then number of spectral lines is given by formula {(n1-n2)(n1-n2+1}/2. so consider a electron jump from 4th shell to 2nd shell then number of kinds of jump can be (1) 4th to 3rd,(2) 4th to 2nd So there are only two jumps. but if we apply formula then it will come out to be 3. So where i or formula is wrong.
thanks for any kind of help.

what about 3rd to 2nd?
 
SpectraCat said:
what about 3rd to 2nd?

dear 4th 3rd and 2nd represent the energy level of hydrogen atom n1 and n2 represent the given energy level. Do you got it.
 
vkash said:
dear 4th 3rd and 2nd represent the energy level of hydrogen atom n1 and n2 represent the given energy level. Do you got it.

Yes, "I got it". You asked what the "third" transition was that is possible in the manifold of levels including 4,3, and 2. I told you the answer. The formula is correct, you just missed a transition with your initial analysis.
 
SpectraCat said:
Yes, "I got it". You asked what the "third" transition was that is possible in the manifold of levels including 4,3, and 2. I told you the answer. The formula is correct, you just missed a transition with your initial analysis.
what's that transition is that 3rd to 2nd. other transitions are already mentioned above.
 
vkash said:
what's that transition is that 3rd to 2nd. other transitions are already mentioned above.

Do you understand what you already wrote? I mean from the 3rd shell to the 2nd shell. Just like you "already mentioned" 4th shell to 3rd shell, and 4th shell to 2nd shell.

Draw yourself a picture, using stacked horizontal lines to represent the states (2, 3 and 4), and downward arrows to represent the transitions. You should see that there are 3 possibilities almost immediately.
 

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