Download Bohr`s atomic model

at a glance
4
Bohr’s atomic model
Line spectra of hydrogen, helium and mercury
6
Orbiting electrons in hydrogen pictured as
de Broglie waves
n=3
I
n 1913 Danish physicist Niels Bohr (1) published a groundbreaking atomic model. It got round a problem with
Rutherford’s 1911 model (P HYSICS R EVIEW Vol. 20, No. 3,
pp. 2–5) — a charged particle that accelerates (changes speed
and/or direction) emits electromagnetic radiation, so electrons
orbiting a nucleus should rapidly lose energy and spiral inwards.
1
2
n=2
Linear and angular momentum
mass, m
n=1
speed, v
radius, r
Niels Bohr (1885–1962)
linear momentum,
ρ = mv
Bohr’s first big idea was that angular momentum (2) of
orbiting electrons is quantised, and the only possible orbits have:
nh
(1)
L=
2π
where n = 1, 2, 3… and h is the Planck constant. This means an
orbiting electron can only have certain energies.
Bohr’s second big idea was that an electron in a higher energy
level moves into a lower one by emitting a single photon (3).
Bohr’s model explained atomic line spectra (4) and predicted
the wavelengths of hydrogen light (5).
3
Photons and energy levels
electron energy E4
n=4
E
= ∆E = E4 – E2
photon electron
energy energy
lost
E3
n=3
Dept. of Physics, Imperial College/SPL
angular momentum,
L = mvr
In the 1920s, it was established that a moving particle has
wave properties and its de Broglie wavelength, λdeB, is related to
its momentum, p:
h
(2)
p
An orbiting electron must have a whole number of
wavelengths around the circumference of its orbit (6), otherwise
the wave will interfere destructively with itself. This approach
predicts the same energy levels as Bohr’s model. (You can use
Box 2 to show that Equations 1 and 2 are equivalent.)
λdeB =
5
Bohr’s model cannot explain everything about atoms and
line spectra and it has been superseded by more sophisticated
models, but it was a major advance in atomic theory and
quantum mechanics.
In 1922 Bohr received the Nobel prize for physics. In a
long working life at Copenhagen University he developed
further theoretical ideas and campaigned for the peaceful use
of atomic physics.
For more notes on Bohr’s model, and to see how it can be
used to calculate the hydrogen wavelengths, visit the web pages
linked to this issue of PHYSICS R EVIEW.
PhysicsReviewOnline
Log on to www.philipallan.co.uk/magazines for a
printable PDF of this centre spread.
Light emitted by excited hydrogen atoms in a discharge tube
photon
E = hf = hc
energy
λ
E2
n=2
16
n=1
SPL
TopFoto
lau fer/Fotolia
E1
Physics Review
April 2013
17