The Balmer equation can be extended beyond the visible portion of the electromag

Question

The Balmer equation can be extended beyond the visible portion of the electromagnetic spectrum to include lines in the ultraviolet. What is the wavelength in nanometers of ultraviolet light in the Balmer series corresponding to a value of n = 7?

What I don't understand is that in the answer they put that m = 2, please explain where they got that 2 from.

Below is another problem, and in the answer they put 4 for n, how they got that from, and how you determine that.

What is the longest-wavelength line in nanometers in the infrared series for hydrogen where m = 3?

Explanation / Answer

for n = 4; these are Brackett series

Apply Rydberg Formula

E = R*(1/nf^2 – 1/ni ^2)

R = -2.178*10^-18 J

Nf = final stage/level

Ni = initial stage/level

E = Energy per unit (i.e. J/photon)

(your doubt) --> For Balmer Equation/Lines, recall that n = 2;

E = (-2.178*10^-18)*(1/nf^2 – 1/2 ^2)

for nf = 7 then

E = (-2.178*10^-18)*(1/7^2 – 1/2 ^2)

E = 5.000*10^-19 J/particle

For the wavelength:

WL = h c / E

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

WL = (6.626*10^-34)(3*10^8)/(5.000*10^-19)

WL = 3.975*10^-7 m

to nanometers:

WL = (3.975*10^-7)(10^9) = 397.5 nm

this is now in nm, since this is below 400 nm

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