Calculate Wavelength of 6th Line in Balmer Series

[JJK1503]

Homework Statement

Compute to three significant figures the wavelength of the sixth line in the hydrogen Balmer series.

Homework Equations

1 / lambda = R * ( 1/ n_final^2 - 1 / n_initial^2 )
R = Rydberg constant = 10973731.57 m^-1
lambda = wavelength

The Attempt at a Solution

I set up the Balmer formula I listed above given the info in the problem

1 / lambda = (10973731.57 m^-1) * ( 1/ 2^2 - 1 / 6^2 ) = 1 / 2438607.015555 m^-1

so, lambda = 410.070 nm
or 4.10 x 10^-7 m using 3 sig figs as the question asks for.

Not sure what I am doing wrong. This seems right to me, but it is not.

Any help is appreciated.

 

[Quantum Defect]

Homework Statement

Compute to three significant figures the wavelength of the sixth line in the hydrogen Balmer series.

Homework Equations

1 / lambda = R * ( 1/ n_final^2 - 1 / n_initial^2 )
R = Rydberg constant = 10973731.57 m^-1
lambda = wavelength

The Attempt at a Solution

I set up the Balmer formula I listed above given the info in the problem

1 / lambda = (10973731.57 m^-1) * ( 1/ 2^2 - 1 / 6^2 ) = 1 / 2438607.015555 m^-1

so, lambda = 410.070 nm
or 4.10 x 10^-7 m using 3 sig figs as the question asks for.

Not sure what I am doing wrong. This seems right to me, but it is not.

Any help is appreciated.

The sixth line means the sixth observed line.

Here are the transisitons:
n_i --> n_f
3--> 2 (first line)
4--> 2 (second line)
5--> 2 (third line)
...
Which is the sixth line?

 

[JJK1503]

The sixth line means the sixth observed line.

Here are the transisitons:
n_i --> n_f
3--> 2 (first line)
4--> 2 (second line)
5--> 2 (third line)
...
Which is the sixth line?

And the hand meets the forehead...
It states the 6th line of the Balmer series not the sixth quantum level.
Thank you for your help, I had a feeling it was something simple.

 

[Quantum Defect]

And the hand meets the forehead...
It states the 6th line of the Balmer series not the sixth quantum level.
Thank you for your help, I had a feeling it was something simple.

We have all done things like this.