Finding The Spectral Line Width

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SUMMARY

The spectral line width for the 5 to 2 transition in hydrogen can be calculated using the uncertainty principle, which relates energy spread (ΔE) to lifetime (ΔT). Given the lifetimes of the states, 7.52 ns for n=5 and 1.38 ns for n=2, the total lifetime is 8.9 ns. The calculated energy spread is ΔE = h/ΔT = 4.63 x 10-7 eV, confirming the relationship between energy and time in quantum mechanics.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically the uncertainty principle.
  • Familiarity with the concept of energy levels in hydrogen.
  • Knowledge of Planck's constant (h) and its application in quantum calculations.
  • Basic proficiency in using equations related to wave packets and energy spread.
NEXT STEPS
  • Study the uncertainty principle in detail, focusing on its implications in quantum mechanics.
  • Learn about the energy level transitions in hydrogen and their significance in spectroscopy.
  • Explore the derivation and application of the equation ΔX = h/p in quantum physics.
  • Investigate the relationship between lifetime and spectral line width in various atomic systems.
USEFUL FOR

Students and professionals in physics, particularly those studying quantum mechanics and atomic spectroscopy, will benefit from this discussion.

Dew.J
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Homework Statement



Using only the information above (previous problem), what is the line width of the spectral line representing the 5 to 2 transition in H (hydrogen)

Homework Equations


Given Data: lifetime of n = 5 is 7.52ns
lifetime of n = 2 is 1.38ns
Thus, total t = 8.9ns

delta E = h/delta T = 4.63x10-7 eV


The Attempt at a Solution



looking through the book I find that Delta X (width of the wave packet) = h/p where p = SQRT(2*Me*E). However, i can find no equation that expressly relates the width of the spectral line. Is this Delta X what I am looking for or is their another equation that I'm not seeing. Thanks.
 
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Hi,
I guess your delta E = h/delta T = 4.63x10-7 eV can be correct!
Or better:
Use the uncertainty principle that related spread of energy and life time! Also take care of notations like h or hbar.
 

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