Question

If λ and λ' are the wavelengths of the third member of Lyman and the first member of the Paschen series respectively, then the value of λ' is:

a. λ/4
b. 4λ
c. 16λ
d. 64λ

Answer 1

The wavelength λ' for the first member of the Paschen series is 18 times the wavelength λ of the third member of the Lyman series, which is not one of the provided options.

Step-by-step explanation:

If λ and λ' are the wavelengths of the third member of the Lyman series and the first member of the Paschen series respectively, we use the Rydberg formula for hydrogen:

R = 1.097 x 107 m-1

For the Lyman series: 1/λ = R(1/12 - 1/n2)

For n = 3 (the third member): 1/λ = R(1 - 1/9) = 8R/9

For the Paschen series: 1/λ' = R(1/32 - 1/n2)

For n = 4 (the first member): 1/λ' = R(1/9 - 1/16) = 7R/144

Now, to find λ' in terms of λ, equate the R terms and solve for λ':

8R/9λ = 7R/144λ'

λ' = 144/7 x 9/8λ = 18λ

None of the given options a. λ/4, b. 4λ, c. 16λ, and d. 64λ, match the correct answer. Therefore, the value of λ' is actually 18 times the value of λ, which is not listed in the given options.