Question

ou plan to excite electrons in a material by exposing it laser radiation. If you want to jump electrons from the 2 shell to the 6 shell, what wavelength of laser should you use

Answer 1

`410.2 nm`

Step-by-step explanation:

We are given that

`n_1=2,n_2=6`

We have to find the wavelength of laser should you used.

We know that

`(1)/(\lambda)=R((1)/(n^2_1)-(1)/(n^2_2))`

Where
`R=1.097* 10^7/m`=Rydberg constant

`\lambda`=Wavelength

Using the formula

`(1)/(\lambda)=1.097* 10^7((1)/(2^2)-(1)/(6^2))`

`(1)/(\lambda)=1.097* 10^7((1)/(4)-(1)/(36))`

`(1)/(\lambda)=1.097* 10^7((9-1)/(36)=1.097* 10^7* (8)/(36)`

`(1)/(\lambda)=(1.097* 10^7)/(4)`

Using identity:
`(1)/(a^x)=a^(-x)`

`\lambda=(4)/(1.097)* 10^(-7)`=
`4.102* 10^(-7) m`

1 nm=
`10^(-9) m`

`\lambda=4.102* 100 * 10^(-9)=410.2* 10^(-9)` m=410.2 nm

Hence, the wavelength of laser=
`410.2 nm`