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What Lavelle has taught us in class is the empirical version of the Rydberg equation. You can still use the equation lavelle showed us in class to solve the problem but it would just take a few more steps than how the solutions manual showed it with just plugging it all into the original version of the rydberg equation.
Because E=hvand E=hR[z], the first equation can be rewritten as v=R[z]. Also because (Lambda)x(frequency)=c, Bohr's equation can be written as c/(Lambda)=R[z].
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