As you i just disputed in the Spectral present page, electrons autumn to lower energy levels and give turn off light in the type of a spectrum.

You are watching: How to find n initial from wavelength

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These spectral lines room actually certain amounts of energy for as soon as an electron transitions come a lower energy level. If you i think the power levels of one atom to be a staircase; if you roll a sphere down the stairs the round only has actually a few "steps" the it have the right to stop on. This is the same case an electron is in. Electrons have the right to only occupy specific energy level in an atom. It many be ~ above an energy level if that is in the atom. Over there is no in between. This is why you gain lines and also not a "rainbow" of colors once electrons fall.

Jahann Balmer in 1885 acquired an equation to calculate the visible wavelengths the the hydrogen spectrum displayed. The lines that appear at 410nm, 434nm, 486nm, and also 656nm. These electrons room falling come the 2nd energy level from greater ones. This change to the 2nd energy level is now referred to together the "Balmer Series" of electron transitions.

Johan Rydberg use Balmers work to obtained an equation for all electron transitions in a hydrogen atom.

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Here is the equation:

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R= Rydberg continuous 1.0974x107m-1; λis the wavelength; nis equal to the power level (initial and also final)

If we want to calculate energy we can change R through multipling by h (planks constant) and also c (speed the light)

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Now we have actually Rydbergs equation to calculate energy.

RE= -2.178 x 10-18J (it is negative because power is gift emitted)

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l = h c /E

l = ( 6.626 x 10- 34J s) (3.0 x 108m/s)/E

1nm= 1 x 10-9m

Electron TransitionEnergy (J)Wavelength (Meters)Wavelength (nm)Electromagnetic region
Paschen collection (to n=3)
n=4 come n=31.06 x 10-191.875 x 10-61875Infrared
n=5 to n=31.55 x 10-191.282 x 10-61282Infrared
Balmer collection (to n=2)
n=3 come n=23.03 x 10-196.56 x 10-7656visible
n=4 come n=24.09 x 10-194.86 x 10-7486visible
n=5 to n=24.58 x 10-194.34 x 10-7434visible
n=6 to n=24.84 x 10-194.11 x 10-7411visible
Lyman series ( to n=1)
n=2 to n=11.632 x 10-181.22 x 10-7122Ultraviolet
n=3 come n=11.93 x 10-181.03 x 10-7103Ultraviolet
n=4 to n=12.04 x 10-189.73 x 10-897.3Ultraviolet
n=5 to n=12.09 x 10-189.50 x 10-895.0Ultraviolet
Converting Wavelength to frequency
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c= 3.0 x 108m/s ;l = wavelength (m) ;v= frequency (s-1)
Wavelength (m)Frequency (s-1)
1.875 x 10-61.6 x 1014
1.282 x 10-62.34 x 1014
6.56 x 10-74.57 x 1014
4.86 x 10-76.17 x 1014
4.34 x 10-76.91 x 1014
4.11 x 10-77.30 x 1014
1.22 x 10-72.45 x 1015
1.03 x 10-72.91 x 1015
9.73 x 10-83.08 x 1015
9.50 x 10-83.15 x 1015
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