Download Chapter 30: The Nature of the Atom Very schematic picture of an atom

Chapter 30: The Nature of the Atom
• Rutherford scattering and the nuclear atom –"the nucleus is really
# small!
• Atomic line spectra – wavelengths characteristic of each element
• Bohr model of the hydrogen atom –"
# quantization of angular momentum ! quantization of energy
• x-rays
• The laser, holograms
• Omit 30.5, 6 – quantum mechanical picture of H-atom, Pauli
! Exclusion Principle, periodic table
1
Very schematic picture of an atom
Size of the nucleus ! 10-15 – 10-14 m
Size of the atom ! 10-10 m
In the normal state, the atom is
electrically neutral – equal amounts of
+ and – charges.
Used to be thought that the + and –
charges occupied the whole volume of
the atom – a positively-charged
“pudding” with negatively-charged
electron “plums” embedded in it
(“plum pudding” model). This was
ruled out by Rutherford following
experiments by Geiger+Marsden...
(charge +Ze)
2
Geiger+Marsden: Scattering of alpha particles
Alpha (!) particles – nuclei of
4He atom, emitted by some
radioactive nuclei.
!-particles scattered from a thin
gold foil and were observed on
a screen. Far more were
scattered at large angle than
would be possible with the
weak electric field inside a
“plum pudding” atom.
Rutherford: the positive charges
of the atom had to be confined
in a very small volume – the
nucleus.
" planetary model of the atom with electrons
# in orbit around nucleus
3
Problem with a Planetary Model of the Atom
• Electrons orbit a positively-charged nucleus.
• The electrons suffer centripetal acceleration in their orbits.
• Any accelerated charge should radiate electromagnetic energy.
" The electrons should lose energy and spiral into the nucleus in very
# # little time.
" A planetary atom should not be stable!
" Classical theory does not explain the structure of the atom.
" Small systems, such as atoms, must behave differently from large.
30.1
4
Prob. 30.1: The nucleus of the hydrogen atom has a radius of about
10-15 m. The electron is normally at a distance of about 5.3$10-11 m
from the nucleus.
Assuming the hydrogen atom is a sphere of radius 5.3$10-11 m, find:
a) the volume of the atom,
b) the percentage of the volume of the atom that is occupied by the
nucleus.
Prob. 30.3: What is the ratio of the density of the hydrogen nucleus to
the density of the complete hydrogen atom?
5
Prob. 30.6: There are Z protons in the nucleus of an atom, where Z is the
atomic number of the element. An ! particle (nucleus of He atom) carries
a charge +2e.
In a scattering experiment, an ! particle, heading directly toward a
nucleus in a metal foil, will come to a halt when all the particle’s kinetic
energy is converted to electric potential energy.
How close will an ! particle with kinetic energy of 5$10-13 J come to a
gold nucleus (Z = 79)?
6
Atomic Line Spectra
Pass a current through low pressure gas. Light is emitted at particular
wavelengths that are characteristic of the chemical element.
The spectrum of sunlight is continuous – blackbody radiation. In addition,
dark (Fraunhofer) lines are visible. They are due to absorption of light by
chemical elements in the “atmosphere” of the sun. This was how helium was
discovered.
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Line spectrum of the hydrogen atom
n=2
m=1
Ultraviolet
n=4
m=2
n=3
Visible
n=6
n=5
n=%
series limit
m=3
n=4
Infrared
Balmer found by trial and error a simple formula to calculate the wavelength
of all lines of the hydrogen atom:
m Series
!
"
1
1
1
1 Lyman ultraviolet
=R
−
m = 1, 2, 3 . . .
!
m2 n2
2 Balmer
visible
n = m + 1, m + 2, m + 3 . . .
3 Pasche
infrared
R = Rydberg constant = 1.097 $ 107 m-1
4 Bracket
infrared
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!
1
1
1
=R
− 2
2
!
m
n
"
Spectrum of H-atom
m = 1, 2, 3 . . .
n = m + 1, m + 2, m + 3 . . .
R = Rydberg constant = 1.097 $ 107 m-1
Example: Lyman series, m = 1:
For n = %:
!
"
1
1 1
7
= 1.097 × 10
−
= 1.097 × 107
2
!
1
"
(serieslimit)
limit, shortest wavelength in Lyman series)
! = 91.2 nm (series
For n = 2:
!
"
1
1
1
7
= 1.097 × 10
− 2 = 0.823 × 107
2
!
1
2
! = 121.5 nm (longest wavelength in Lyman series)
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