Value of n for the energy level transition that produce lamb

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SUMMARY

The discussion centers on determining the initial and final quantum numbers (n) for the energy level transition of a hydrogen atom that emits a wavelength of 410.2 x 10^-9 m. The Rydberg formula, specifically 1/(lambda) = R * (1/2^2 - 1/n^2), is utilized to solve for n. The correct values are identified as ni = 6 and nf = 2, indicating a transition from the sixth to the second energy level. This conclusion is reached by recognizing the emission corresponds to the Lyman series for hydrogen.

PREREQUISITES
  • Understanding of quantum mechanics and energy levels in atoms
  • Familiarity with the Rydberg formula for hydrogen
  • Knowledge of the Lyman series and its significance in atomic transitions
  • Basic proficiency in solving algebraic equations
NEXT STEPS
  • Study the Rydberg formula in detail, including its derivation and applications
  • Explore the different series of hydrogen emissions: Lyman, Balmer, and Paschen
  • Learn about quantum numbers and their physical significance in atomic structure
  • Investigate the implications of high voltage discharge tubes in atomic spectroscopy
USEFUL FOR

Students of physics, particularly those studying quantum mechanics, as well as educators and anyone interested in atomic spectroscopy and energy level transitions in hydrogen.

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Homework Statement



A wavelength of 410.2*10^-9m is emitted by the hydrogen atom in a high voltage discharge tube. what are the initial and final values of the quantum number n for the energy lvl transition that produces this wavelength?

Homework Equations


1/(lambda) = R * (1/2^2 - 1/n^2): Lyman series?

The Attempt at a Solution


I have used this equation to figure out (lambda) but never the other way around.
I tried to solve for n but it doesn't make sense. How can I know which series to solve n for?
At first I thought that it had to be Lyman as Z=1 for hydrogen and subsequently n=1 but no.
The answer is ni = 6 and nf = 2.
 
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use Rydberg eq.

r.JPG

RH=10973732 m^(-1)
 

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