Question

HOw to calculate Corrected Observed Hydrogen Wavelengths (nm) and Theoretical Hydrogen Wavelengths (nm)?

Answer 1

The Hydrogen spectrum wavelength can be determined using Rydberg formula:

λ is the wavelength of the emitted photon
R = Rydberg's constant (1.097 x 10⁷ m^-1)
Z = atomic number of the atom ( Z= 1 for Hydrogen)
n_f and n_i are integers n_i > n_f.

n_f and n_i represents principal quantum number of the corresponding energy states between which transition(or emission) takes place.

Using this formula we can obtain theoretical wavelength values of hydrogen spectral lines. In the spectrum, we get different series of lines.

nf	ni	Wavelength(nm)	Series
1	2,3,4…	91 (UV)	Lyman
2	3,4,5…	365 (VISIBLE)	Balmer
3	4,5,6…	820 (IR)	Paschen
4	5,6,7…	1458 (FAR IR)	Brackett
5	6,7,8…	2278 (FAR IR)	Pfund
6	7,8,9…	3280 (FAR IR)	Humphereys

The above table shows the wavelength corresponding to a hydrogen spectral lines originating from any higher energy level (n_i ) to lower energy level n_f =1, this series of spectral lines are called Lyman series.

Similarly for n_f =2 , Balmer series and so on.

Example: To find the wavelength of first line of Balmer series.

Here, n_f =2       n_i = 3

Rydberg formula

λ= 656 nm

Similarly you can calculate the theoretical values of wavelengths of different spectral lines.

By using a Spectrometer you can experimentally determine the Hydrogen spectral line wavelength.

Each spectral series would have different colors.

You can obtain the wavelength(nm) of a particular spectral line from spectrometer reading and compare with the theoretical value.

The difference between the two values give the value of error ( which is usually very small ).