wavelength

Question

These are all lines observed that correspond to the emission spectrum when an excited one electron ion relaxes to the n = 4 state. The wavelength of the B line is 455nm. What is the wavelength on the A line 

 

 

 

     B           A

...  .     .      .        .           .

 

These dots are wavelengths 

Answer 1

From the diagram, it looks like n_iB = 9 and n_iA = 7 (counting from right to left, with the first line starting at n_i = 5 > 4).

 

B line:

 

1/455 = K(1/4² - 1/9²)

 

K = 0.0438208

 

A line:

 

1/λ = 0.0438208(1/4² - 1/7²)

 

λ_A = 542 nm