An atomic emission spectrum of hydrogen shows the following threewavelengths: 12

Question

An atomic emission spectrum of hydrogen shows the following threewavelengths: 121.5 nm, 102.6 nm, and 97.23 nm. Assign thesewavelengths to transitions in the hydrogen atom.

choose the correct answer in each case
A
For 121.5 nm
n=2 ----> n=1
n=3 ----> n=1
n=4----> n=1
n=5 ----> n=1

B
For 102.6 nm
n=2 ----> n=1
n=3 ----> n=1
n=4----> n=1
n=5 ----> n=1

C
For 97.23 nm
n=2 ----> n=1
n=3 ----> n=1
n=4----> n=1
n=5 ----> n=1

Explanation / Answer

we know that 1/ = R ( 1/ n12 - 1/ n22) where R is Rydbergs constant value = 109678 cm-                                                       = 10967800 m- now n1 = 1 in each case so putting down the values we get: 1) = 121.5 nm        = 121.5 x 10-9m so 1/121.5 x 10-9 m = 10967800 m- ( 1 -1/ n22) n2 ~= 2 so answer is For 121.5 nm n=2 ----> n=1 2) = 102.6 nm       = 102.6 x 10-9 m so 1/ 102.6 x 10-9 m = 10967800 m- ( 1 - 1/n22) n2 ~= 3 so answer is : n=3 ----> n=1 3) = 97.23 nm       = 97.23 x 10-9 m so 1/97.23 x 10-9 m = 10967800 m- ( 1 - 1/n22) n2 ~ = 4 so answer is: n=4----> n=1

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