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Background: The visible spectrum of hydrogen can be described accurately with an

ID: 1684935 • Letter: B

Question

Background:
The visible spectrum of hydrogen can be described accurately with an empirical formula found by the Swiss teacher Johann Balmer in 1885. This formula, which gives the wavelength of a spectral line as a function of an integer quantity n, describes the spectrum known as the Balmer series. By varying n, you can calculate the wavelength of all spectral lines.

Question:
Find the minimum value of n in the Balmer series for which the predicted wavelength is in the ultraviolet region of the spectrum.

n=_________

I have tried 8 and 9, but those were wrong. Can anyone help me out?

Explanation / Answer

Balmer says: empiric wavelength
= 3645.5·10^(-10) /(1-4/n^2) in meter units,
while longest UV wave length L=4·10^(-7) m;
thus you are demanded to find n when < L;


3.6455·10^(-7) /(1-4/n^2) < 4·10^(-7);
3.6455/4 < 1-4/n^2; 4/n^2 < 1-0.911375; n^2 > 45.134; n > 6.7;
since n is integer by nature, then n > 6; thus your n=7;