Question

What is the wavelength, in nm, of the line in the hydrogen spectrum when one n value is 3 and the other n value is 6?

Answer 1

`\lambda=1090nm`

Step-by-step explanation:

Rydberg formula is used to calculate the wavelengths of the spectral lines of many chemical elements. For the hydrogen, is defined as:

`(1)/(\lambda)=R_H((1)/(n_1^2)-(1)/(n_2^2))`

Where
`R_H` is the Rydberg constant for hydrogen and
`n_1`,
`n_2` are the lower energy state and the higher energy state, respectively.

`(1)/(\lambda)=1.10*10^(7)m^(-1)((1)/(3^2)-(1)/(6^2))\\(1)/(\lambda)=9.17*10^(5)m^(-1)\\\lambda=(1)/(1.09*10^(6)m^(-1))\\\lambda=1.09*10^(-6)m*(10^(9)nm)/(1m)\\\lambda=1090nm`