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bobby.pdx

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## Homework Statement

Derive from the uncertainty principle a formula for the relative spread of the spectral line that corresponds to the longest wavelength of the Lyman series.

## Homework Equations

uncertainty principle:

σ

_{x}σ

_{p}≥[itex]\hbar[/itex]/2

planck constant

[itex]\hbar[/itex]=h/2pi

h=λp

Lyman series:

1/λ=R

_{H}(1-1/n

^{2})

λ=hc/E

_{i}-E

_{f}

## The Attempt at a Solution

I'm not quite sure how to go about the problem. I have gathered some formulas I believe will help me out. If I substitute some of these formulas into the uncertainty principle I get

σ

_{x}σ

_{p}≥(hc/E

_{i}-E

_{f})p/(4pi)

I'm not sure where to go from here. Any help would be greatly appreciated.