If, in you set n1 = 1 and take n2 greater than 1 , you generate what is known as

Question

If, in you set n1 = 1 and take n2 greater than 1 , you generate what is known as the Lyman series. Findthe wavelength of the first mem- ber of this series. The value of ¯h is 1.05457× 1034 J · s ; the Rydberg constant for hydrogen is 1.09735 × 107 m1 ; theBohr radius is 5.29177 × 1011 m; and theground state energy for hydrogen is 13.6057 eV. Answer in unitsof nm.
Consider the next three members of this series. Thewavelengths of successive members of the Lyman series approach a common limit as n2 !1. What is this limit? Answer in units of nm.

Explanation / Answer

You can rewrite the the equation as = (1 / R ) n12 *n22 / (n22 -n12) 21 = 1 * 4 / *(4 - 1) * 1/R = 4 / (3 R) =121.50 nm using 1 / R from below 31 = 1 * 9 / (9 - 1) * 1/R = 9 / (8 R) 31 = 1 * 16 / (16 - 1) * 1/R = 16 / (15R) 1 = 1/R 1 / R = 1 ( 1.09735 * 10E-7) = 91.1286 * 10E-9 = 91.1286nm

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