25.THE ATOMIC STRUCTURE – The Bohr Model(3)

Niels Bohr brought a revolution by making necessary amendments in the Rutherford’s nuclear model and later proposing his own model. His theoretical predictions were authenticated by experimental data too.Let us begin this post by studying the hydrogen atom spectra with reference to the Bohr Model.

FYI

spectral_lines_en

Type of Substance

Type of spectrum

Hot opaque Body e.g. a dense gas/solid

continuous spectra,like rainbow of colors.

Hot transparent gas e.g. Hydrogen gas in a gas discharge tube

emission spectra- specific lines on a dark background.

Cool transparent gas(source of light continuous)

Absorption spectra – dark lines between the colors of continuous spectra.

The discreet lines in the emission spectrum occur at exactly the same wavelengths as the dark lines in the absorption spectrum.

H- atom spectra and the Bohr Model :-

We already know that ,according to Bohr Model , E(n) = – RH2/n2).

For H- atom in the gas phase , Ƶ=1 (as atomic number of hydrogen is 1).

So, for H-atom, E(n) = – RH/n2.

Now, using this formula let us try to find energies for different orbits in the hydrogen atom.

Note ⇒  RH = 1.1 ×107 m -1 =2.18 x 1018 J = 13.6 eV.

Energy for the first orbit i.e the orbit closest to the nucleus, n=1.

∴ E(1) =- RH/(1)2 = -13.6/1 = -13.6 eV.

For n=2, E(2) =- RH/(2)= -13.6/4 = -3.4 eV.

For n=3, E(3) =- RH/(3)= -13.6/9 = -1.511 eV.

Note that all values of E are negative.As the value of n ↑ , value of energy also goes up(-1.511 > -13.6).

251
Hydrogen atom energy levels.

We have already studied that when the ground state electron in H-atom is excited by input of energy, it falls back down to the ground state emitting electromagnetic radiation (EMR) of energy.This phenomenon of excitation and falling back of the electrons gives rise to the atomic spectra. We get lines of definite colors i.e definite wavelengths(every color has a definite wavelength,λ.e.g. the red line in H- atom spectra has a λ = 656nm).These lines are unique to an element.Thus, by observing these lines we can find out the element under study.

The line spectra of hydrogen

We have already seen that ,

rydberg-formula

where the wave number is reciprocal of the wavelength.

∴1/λ = RƵ2 {(1/n2f – 1/n2i)}.

The emission spectra of atomic H-atom thus can be  divided into a number of spectral series, with wavelengths given by the above formula.The series are as follows –

Date of discovery

Series

Region

n1

n2

1906-1914

Lyman

UV

1

2,3,4..

1885

Balmer

Visible

2

3,4,5

1908

Paschen

IR

3

4,5..

1922

Brackett

IR

4

5,6…

1924

Pfund

Far IR

5

6,7..

Humphrey

far IR

6

7,8..

How do we know in which region we can find the emissions? Theorotically we can calculate the regions using the Bohr formula and Rydberg equation.

e.g. – For Balmer series, electron falls from n=3 to n=2. We have already calculated energies   for these orbits above.

Thus, ΔE = E3-E2
= -1.511-(-3.4)
= 1.8eV
eV is NOT a SI unit, so ,converting this energy into joules, (1eV= 1.6×10-19J).

∴1.8eV = 1.8× 1.6×10-19J =29.76 ×10-19J.

We know that ,  ΔE =hc/λ .

∴ λ= hc/ΔE.
=(6.626 ×10-34×3×108)/29.76×1019.
       ≈660nm ⇒ VISIBLE RANGE⇒ This corresponds to the red line in the Balmer series.253

The first series discovered was by Ångström, as he could see the discrete lines in the visible range of the spectrum.He could have found out the first series where electrons fall down to n=1 too! But unfortunately, he was using a photographic plate to detect the emissions which could only record the emissions in the visible region.

246

n=3 → n=2 ⇒ 410nm 
n=4→ n=2⇒ 434 nm
n=5→ n=2⇒ 486 nm
n=6→ n=2⇒ 656 nm.

The 4 lines in the Balmer series are named as  Hα ,Hβ,H𝞬 and Hδ lines.

 

There was still more evidence in support of the Bohr Model.A year later after Bohr model was proposed, James Franck and Gustav Hertz conducted the Franck-Hertz experiment(1914).

In their experiment, they used a drop of mercury metal(vapour) in a vacuum tube.They introduced two electrodes, cathode and anode in the tube and connected them to a variable voltage source.They also introduced in the circuit an ammeter to measure the electric current.

254

They studied the variation of current(i) with the changing voltage(v).This is what they observed –

261

At first they observed that they got low current at low voltage and current increased as they increased the voltage.This was as expected.But as they kept increasing the voltage, at some critical volatge value(4.9V), the current almost dropped to zero and the tube started glowing! At this stage, they again kept increasing the voltage and saw that again the current  showed a rise with the increase in voltage and at another critical point(6.7V) dropped  almost to zero again ! The tube started glowing more brilliantly than before!Thus, this phenomenon showed a periodic behaviour.
The ionisation energy of mercury is 10.4 eV. These values recorded were less than the ionisation energies ! So, they reasoned that electrons in the mercury atom were excited within the atom and and as this happens only at certain discrete values, the energy levels within the atom must be quantised too ! Though at the time of the experiment , both Franck and Hertz had not known about the Bohr Theory, they later adopted this theory as a possible explanation to the phenomenon they saw.Also, in 1915, Bohr  published a paper noting that the measurements of Franck and Hertz were consistent with his own model for atoms. Franck and Hertz’s observed  emission  at 254 nm from the tube. When the calculations were done according to the Rydberg equation and Bohr model concept, the values of λ matched. Thus, this experiment showed that the energy level quantisation concept proposed for an one electron atom was true for multi electron atoms too ! Thus, all atoms have quantised energy levels ! The Franck-Hertz experiment thus became one of the most important experimental pillars of quantum mechanics.On December 10, 1926, Franck and Hertz were awarded the 1925 Nobel prize in Physics “for their discovery of the laws governing the impact of an electron upon an atom.”

This concept gave birth to the new world of Quantum Mechanics.Thus , Neils Bohr is correctly called as ‘The Father Of Quantum Mechanics’! Niels Bohr won a Nobel prize in Physics in 1922.

LIMITATIONS OF BOHR MODEL –

Though this theory was a huge step forward it had some limitations. The Limitations of The Bohr model were as follows –

1)This theory could not explain multi-electron systems.

2)The theory could not explain the relative intensities of the spectral lines.Some lines  are more intense than the others.In 1887,in Case University,Mchelson and Morley (First american to win a Nobel prize) found out that the intense spectral lines were in fact a DOUBLET ! The Bohr model was incapable of explaining this hyperfine structure of the spectral lines.

3)Under a magnetic field and in an electric field, the spectral lines exhibit a splitting phenomenon.

Splitting of spectral lines in a magnetic field – ZEEMAN EFFECT.
Splitting of spectral lines in an electric field – STARK EFFECT.

Both the above effects could not be explained by the Bohr atomic Model.

So, obviously there was a lot more to be discovered about this small indivisible particle of matter – the atom.What were the further developments? We shall find that out in our next post. Till then,

Be  a pertpetual student of life and keep learning…

Good Day !

 

References and Further Reading –

1)http://astro.unl.edu/naap/hr/hr_background1.html

2)Lec 5 ,MIT 3.091SC Introduction to Solid State Chemistry, Fall 2010 by professor Donald Sadoway.

3)https://en.wikipedia.org/wiki/Franck–Hertz_experiment

Image source –

1)http://astro.unl.edu/naap/hr/hr_background1.html

2)https://en.wikipedia.org/wiki/James_Franck#/media/File:James_Franck_1925.jpg

3)https://en.wikipedia.org/wiki/Gustav_Ludwig_Hertz#/media/File:Gustav_Hertz.jpg

4)https://en.wikipedia.org/wiki/Franck–Hertz_experiment#/media/File:Franck-Hertz_en.svg

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