Question

Question #01511

Answer 1

Three spectral lines
4 => 3 transition is in Infrared spectrum `(lamda = 1890 nm)`
4 => 2 transition is in the Visible spectrum `(lamda=488nm)`, and
4 => 1 transition in the Ultra Violet Spectrum `(lamda= 97nm)`.

Explanation:

One can calculate the wavelength of each transition using the equation
`1/lamda` = `R_H` `(1/n_f^2 - 1/n_i^2)`; `R_H = 109,678cm^-1`.

4 => 3 transition
=> `1/lamda` = `109,678cm^-1(1/(3)^2 - (1/(4)^2)` = `5265cm^-1`

=> `lamda` = `1.89xx10^-4cm` = 1890 nm (IR wavelength)

4 => 2 transition
=> `1/lamda` = `109,678cm^-1(1/(2)^2 - (1/(4)^2)` = `2051cm^-1`

=> `lamda` = `4.88xx10^-5cm` = 488 nm (Visible wavelength)

4 => 1 transition
=> `1/lamda` = `109,678cm^-1(1/(1)^2 - (1/(4)^2)` = `5265cm^-1`

=> `lamda` = `9.73xx10^-6cm` = 97 nm (UV wavelength)