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FEW EVIDENCES IN FAVOR OF BOHR’S THEORY:
(i) Ratio of mass of electron to the mass of the proton:
m
:
MH
The difference in the Rydberg constant for H- atom and He- atom can be used to
Determination of
compute the ratio of the mass of the electron to the mass MH of the hydrogen nucleus
(proton).
We have
RH =
Rα
........................(1)
m
1+
MH
Rα
..............(2)
m
1+
M He
Where Rα = Rydberg constant for an infinitely heavy nucleus.
And RHe =
Since the mass of the He - nucleus is four times that of the H-atom; we can write,
RHe =
Rα
m
1+
4M H
∴ (1) ÷ (2) ⇒
m
1+
4M H
4M H + m
RH
=
=
4 ( M H + m)
RHe 1 + m
MH
7
−1
R − RH
1 RH = 1.09677 × 10 m
m
= He
=
1836 RHe = 1.09622 × 107 m −1
MH R − 1 R
H
He
4
This agrees with the expected result.
⇒
Thus knowing RH and RHe the ratio
m
MH
Again The specific charge of electron;
Few evidences in favour of Bohr’s theory: S. A. Hussain
i
e
e MH
.............(4)
=
m
m
mH
e
(specific charge of H-atom or the charge required to liberal 1 gm equivalent of
MH
any substance and is known as Faraday constant) is given by,
Now
e
= 96500 coulomb/gram
MH
and
m
1
=
M H 1836
∴ From (4) ⇒
e 96500
=
= 1.77 × 108 coulomb/gram
1
m
1836
(ii) Discovery of heavy hydrogen:
The careful investigations of Aston, Brige and Benzel, Urey, Brickwedde and
Murphy led to the discovery of an isotope of hydrogen. It was observed that naturally
occurring hydrogen, e.g. in water, consisted of normal hydrogen of mass 1 together with
an isotope of mass number 2 known as heavy hydrogen or deuterium expressed as 1D2. In
the spectrum of natural hydrogen, the lines due to deuterium should be observed slightly
displaced from the corresponding lines of hydrogen proper because of the little effect of
large nuclear mass. Urey and his co workers observed that the intensity of lines which are
slightly shifted towards the shorter wave length side is extremely less than the
corresponding hydrogen lines. This is because of the poor abundance of deuterium in the
natural hydrogen, nearly one in 5000 atom. The hydrogen artificially enriched with
deuterium shown an increase in the intensity of the additional lines. In the case of first
line of the Balmer series the separation between the lines Hα and Dα is of the order of
1.79 A0. The separation can be computed as
Few evidences in favour of Bohr’s theory: S. A. Hussain
ii
uuuur uuuur
vDα − vHα =
Rα ⎛ 1
Rα ⎛ 1
1 ⎞
1 ⎞
− ⎟−
− ⎟
⎜
⎜
2
2
2
m ⎝2
3 ⎠ 1+ m ⎝ 2
32 ⎠
1+
MH
MD
⎡
⎤
⎢
r
⎛ 1
1 ⎞
1
1 ⎥
⎥
⇒ ∆v = Rα ⎜ − ⎟ ⎢
−
m ⎥
⎝ 22 32 ⎠ ⎢1 + m
1+
⎢⎣ M H
M D ⎥⎦
= Rα .
5 1
.
36 3683
ur
∴∆λ ≈ 1.79 A 0
Rα = 1.09737 × 107
Thus we see that the discovery of heavy hydrogen or deuterium is another success of
Bohr theory.
(iv) Specific charge of electron:
For the specific charge of the electron we can write,
e
e MH
=
..................(1)
m
m
MH
Also we have already seen that
m
1
=
M H 1837
e
is the charge carried out by one gram ion of hydrogen and is equal to
MH
96495.00 coulombs.
Again
Using these facts we have,
e
= 96495000 × 1837coulomb/kg
m
= 1.77 × 1011 coulomb/kg
e
is very close the theoretically calculated value confirming
m
the success of the Bohr’s theory.
The experimental value for
Few evidences in favour of Bohr’s theory: S. A. Hussain
iii