Question

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Explain the Hydrogen spectrum (as proposed by Sommerfeld under Extension of Bhor's theory).

*With picture*

Answer 1

Hydrogen Spectrum

Niels Bohr introduced the atomic Hydrogen model in 1913. He described it as a positively charged nucleus, comprised of protons and neutrons, surrounded by a negatively charged electron cloud. In the model, electrons orbit the nucleus in atomic shells. The atom is held together by electrostatic forces between the positive nucleus and negative surroundings

The movement of electrons between these energy levels produces a spectrum. The Balmer equation is used to describe the four different wavelengths  of Hydrogen which are present in the visible light spectrum. These wavelengths are at 656, 486, 434, and 410nm. These correspond to the emission of photons as an electron in an excited state transitions down to energy level n=2. The Rydberg formula, below, generalizes the Balmer series for all energy level transitions. To get the Balmer lines, the Rydberg formula is used with an nf of 2.

Answer 2

hello dear sistah..!!

SOMMERFELD MODEL :

• he studied line spectrum of one electron systems using High resolving power spectoscope and he noticed that a line is a collection of more than one fine line nearly of same wavelength. this was called FINE SPECTRUM.

features of sommerfeld model :

• The motion of electron in closed circular orbits is influenced by its own nucleus and is setup into closed elliptical path.

• the angular momentum of an electron in closed elliptical path is quantised. (I. e) { nh/2π}

•the ratio
$\frac{n}{k} \: = \frac{length \: of \: major \: axis}{length \: of \: minor \: axis}$
Thus relation suggest possible number of sub shells in a shell. possible value of k for n =4 are 1,2,3,4 but k not equal to zero.

GENERAL ATOMIC SPECTRA OF HYDROZEN :

• we know that hydrogen has only one electron, yet it's spectrum consists of several lines.

• on passing electric discharge to H2 gas, molecules are dissociated into atoms. the electron of each H-atom is exited to higher state and after some time they return back to lower energy level and emits radiant energy. the radiation thus emitted is called EMMISSION SPECTRUM OF HYDROGEN.

$\gamma = r\: ( \frac{1}{ {n1}^{2} } - \frac{1}{ {n2}^{2} } )$
SERIES :
• lyman series n1=1 ,n2>1 (UV region)
•Balmer series n1=2,n2>2 ( visible region)
•paschen series n1=3,n2>3(near IF region)
•bracket series n1=4,n2>4 (far IF region)
•pfund series n1=5,n2>5. (far IF region)

LIMITATIONS OF BOHR - SOMMERFELD MODEL :

• they could not explain the spectrum of poly electronic systems
•position of electron in an orbit is not fixed around the nucleus.
•these models didn't explain the behaviors of electron in applied electric and magnetic field.
• the repulsion between two electrons in case of poly electronic atoms was not taken into account.

• the picture that I had attached is the sommerfeld model of hydrogen spectrum ( one electron system).

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hope it is useful.....!!!