Question

Ratio of longest to shortest wavelength in Balmer series is ______.

Options

• 5 : 9

• 9 : 5

• 25 : 81

• 81 : 25

Answer 1

Ratio of longest to shortest wavelength in Balmer series is 9 : 5.

Explanation:

For Balmer Series, `1/lambda = "R"(1/2^2 - 1/"n"^2)`

For longest wavelength, n = 3

`1/lambda_"L" = "R"(1/2^2 - 1/3^2)`

`1/lambda_"L" = ("5R")/36`

`lambda_"L" = 36/(5"R")`    ...(i)

For shortest wavelength, n = ∞

`1/lambda_"s" = "R" (1/2^2 - 1/oo^2)`

`=> 1/lambda_"s" = "R"/2^2`

`=> lambda_"s" = 4/"R"`   ...(ii)

Now from (i) and (ii)

`lambda_"L"/lambda_"s" = (36/(5"R"))/(4/"R")`

`=> lambda_"L"/lambda_"s" = 9/5`