Answer :
The wavelength of a line in the spectrum of hydrogen is 6564A° .
Let us consider balmer series for calculating wavelength of a line in the spectrum of hydrogen.
From line spectrum of hydrogen , we know that,
[tex]wave \: number \: = R( \frac{1}{ {n1}^{2} } - \frac{1}{ {n2}^{2} } )[/tex]
where n1 is the lower energy level of balmer series.
n2 is the higher energy level of balmer series.
n1 = 2 , n2 = 3 for balmer series.
R is the Rydberg's constant = 109677 cm^-1
Wave number = 109677 ( 1/2^2 - 1/3^2 ) cm^-1
= 109677 ( 1/4 - 1/9 ) cm^-1
= 109677 ( 5/36 ) cm^-1
= 15232.91 cm^-1
As we know,
wavelength is the reciprocal of wave number.
Thus, wavelength = 1/wave number = (1 /15232.91) cm
wavelength = 6.564733 cm = 6564 A°
Thus, the wavelength of a line in the spectrum of hydrogen is 6564A° .
Hydrogen spectrum is observed by examining the light emitted when a discharged passes through a tube containing hydrogen. the tube contains millions and trillions of atoms in varying states of excitation. these atoms undergo transition from a higher orbit to lower one in a random fashion, thus giving rise to a number of lines.
Wavelength and wave number depends upon the orders of the two orbits between which the transition takes place.
Learn more about wavelength here :
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