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## Homework Statement

The ionisation energy of a single hydrogen atom is 13.6 eV. The application of Bohr quantisation to the hydrogen atom results in the stationary states having discrete energies given in terms of a positive integer

*n*according to

E=-R

_{B}/n

^{2}

where R

_{B}is the Rydberg constant. Determine the value of the Rydberg constant. Assuming like Bohr that, when an atom emits or absorbs radiation, it does so in the form of a single quantum, compute the wavelength of the spectral line of the Balmer series (the transition from n=3 to n=2) for hydrogen.

## Homework Equations

E=-R

_{B}/n

^{2}

[tex]\stackrel{1}{\lambda}[/tex]=R

_{B}[[tex]\stackrel{1}{n

_{1}

^{2}}[/tex]-[tex]\stackrel{1}{n

_{2}

^{2}}[/tex]]

## The Attempt at a Solution

Ok my main issue with this whole question is which value is the Rydberg constant. Is it:

2.18*10

^{-18}J

__or__1.097373157*10

^{7}m

^{-1}(or both)

If I go with the first value, I can easily obtain that using the first equation as it mentions in the equation

*"it does so in the form of a single quantum"*, meaning that n in the equation is equal to 1 and its a simple case of multiplying 13.6 eV by 1.6*10

^{-19}to convert it to joules giving 2.18*10

^{-18}J.

For the second part however I cannot get a reasonable answer using this value of the Rydberg constant, only with the second one as shown below:

*Using first value:*

[tex]\stackrel{1}{\lambda}[/tex]=(2.18*10

^{-18})[[tex]\stackrel{1}{4}[/tex]-[tex]\stackrel{1}{9}[/tex]]

lambda=3.03*10

^{-19}m

*Using second value:*

[tex]\stackrel{1}{\lambda}[/tex]=(1.097373157*10

^{7})[[tex]\stackrel{1}{4}[/tex]-[tex]\stackrel{1}{9}[/tex]]

=656nm (visible)

Im guessing that the constant is both values but I've missed a conversion somewhere. Either that or there is something missing in the second equation to amend this issue with using 2.18*10

^{-18}J.

Finally, how do you do fractions on this properly because as you can see on my post, its seperated each fraction from the equation and has somehow enlarged itself. I havent used this forum that much so i'm still unsure on things like this.

Thanks in advance