Question

What is the frequency and wavelength of a photon emitted during a transition from n = 6 to n = 1 state in the hydrogen atom ?

Answer 1

`v=-3.2*10^15 Hz or s^-1`
`λ=-9.4*10^(-8)m`

Explanation:

Alright, given:
`n_i= 6`
`n_f=1`
`z=1` z is the atomic number
`R_H= 2.179xx10^(-18) J` It is a constant

To find change in energy
`∆E= -Z^2*R_H(1/n_f^2- 1/n_i^2)`
`∆E= -(1)^2*2.179xx10^(-18) J(1/(1)^2- 1/(6)^2)`
`∆E=-2.12*10^(-18)J`

To Find frequency:
`v= (∆E)/h`
h is plank's constant: `6.626*10^(-34) Js`
`v= (∆E)/h`
`v=(-2.12*10^(-18)J)/(6.626*10^(-34) Js)`
`v=-3.2*10^15 Hz or s^-1`

To find wavelength:
`c/v= λ`
Where c is the speed of light, `3*10^8 m/s`
`(3*10^8 m/s)/(-3.2*10^15 Hz)= -9.4*10^(-8)m`