Heisgnberg principle, energy levels & atomic spectra word document full discription on these topics avaivale can be used as presentations or assignments. hope so it may help

1. Physics
Assignment no:1
University of lahore
Name:
Registration no:
Department:
Bs chemistry
Topics:
Uncertainity principle
Atomic spectra
Energy levels of electrons.
What is Heisenberg's Uncertainty Principle?
How the sun shines and why the vacuum of space is not actually empty

2. Equation of this principle:
The uncertainty principle is one of the most famous (and probably
misunderstood) ideas in physics. It tells us that there is a fuzziness in nature, a
fundamental limit to what we can know about the behaviour of quantum
particles and, therefore, thesmallest scales of nature. Of these scales, the most we
can hope for is to calculate probabilities for where things are and how they will
behave. Unlike Isaac Newton's clockwork universe, where everything follows
clear-cut laws on how to move and prediction is easy if you know the starting
conditions, theuncertainty principleenshrines a level of fuzziness into quantum
theory.
Werner Heisenberg's simple idea tells us why atoms don't implode, how the sun
manages to shineand, strangely, that the vacuum of space is not actually empty.
An early incarnation of the uncertainty principle appeared in a 1927 paper by
Heisenberg, a German physicist who was working at Niels Bohr's institute in
Copenhagen at the time, titled "On the Perceptual Content of Quantum
TheoreticalKinematics and Mechanics". The more familiar form of the equation
came a few years later when he had further refined his thoughts in subsequent
lectures and papers.

3. Heisenberg was working throughthe implications of quantum theory, a strange
new way of explaining how atoms behaved that had been developed by
physicists, including Niels Bohr, Paul Dirac and Erwin Schrödinger, over the
previous decade. Among its many counter-intuitive ideas, quantum theory
proposed that energy was not continuous but instead came in discrete packets
(quanta) and that light could be described as both a wave and a stream of these
quanta. In fleshing out this radical worldview, Heisenberg discovered a problem
in the way that the basic physical properties of a particle in a quantum system
could be measured. In one of his regular letters toa colleague, Wolfgang Pauli, he
presented theinklings of an idea that has since became a fundamentalpart of the
quantum description of the world.
The uncertainty principle says that we cannot measure the position (x) and the
momentum (p) of a particle with absolute precision. The more accurately we
know one of these values, the less accurately we know the other. Multiplying
together the errors in the measurements of these values (the errors are
represented by the triangle symbol in front of each property, the Greek letter
"delta") has to give a number greater thanor equalto half of a constant called "h-
bar". This is equal to Planck's constant (usually written as h) divided by 2π.
Planck's constant is an important number in quantum theory, a way to measure
thegranularity of the world at its smallest scales and it has the value 6.626 x 10-
34
joule seconds.
One way to think about the uncertainty principle is as an extension of how we
see and measurethings in theeveryday world. You can read these words because
particles of light, photons, have bounced off the screen or paper and reached
your eyes. Each photon on that path carries with it some information about the
surface it has bounced from, at the speed of light. Seeing a subatomic particle,
such as an electron, is not so simple. You might similarly bounce a photon off it
and then hope to detect that photon with an instrument. But chances are that the

4. photon will impart some momentum to the electron as it hits it and change the
path of the particle you are trying to measure. Or else, given that quantum
particles often move so fast, the electron may no longer be in the place it was
when the photon originally bounced off it. Either way, your observation of either
position or momentum will be inaccurate and, more important, the act of
observation affects the particle being observed.
The uncertainty principle is at the heart of many things that we observe but
cannot explain using classical(non-quantum) physics. Take atoms, for example,
where negatively-charged electrons orbit a positively-charged nucleus. By
classical logic, we might expect the two opposite charges to attract each other,
leading everything to collapse into a ball of particles. The uncertainty principle
explains why this doesn't happen: if an electron got too close to the nucleus, then
its position in space would be precisely known and, therefore, the error in
measuring its position would be minuscule. This means that the error in
measuring its momentum(and, by inference, its velocity) would be enormous. In
that case, the electron could be moving fast enough to fly out of the atom
altogether.
Heisenberg's idea can also explain a typeof nuclear radiation called alpha decay.
Alpha particles aretwo protons and two neutrons emitted by some heavy nuclei,
such as uranium-238. Usually these are bound inside the heavy nucleus and
would need lots of energy to break thebonds keeping themin place. But, because
an alpha particleinsidea nucleus has a very well-defined velocity, its position is
not so well-defined. That means there is a small, but non-zero, chance that the
particle could, at some point, find itself outside the nucleus, even though it
technically does not have enough energy to escape. When this happens – a
process metaphorically known as "quantum tunneling" because the escaping
particlehas to somehow dig its way throughan energy barrier thatit cannot leap
over – the alpha particle escapes and we see radioactivity.

5. A similar quantum tunnelling process happens, in reverse, at the centre of our
sun, where protons fuse together and release the energy that allows our star to
shine. The temperatures at the core of the sun are not high enough for the
protons to have enough energy toovercome their mutual electric repulsion. But,
thanks totheuncertaintyprinciple, they can tunneltheir way throughtheenergy
barrier.
Perhaps the strangest result of the uncertainty principle is what it says about
vacuums. Vacuums are often defined as the absence of everything. But not so in
quantum theory. There is an inherent uncertainty in the amount of energy
involved in quantum processes and in the time it takes for those processes to
happen. Instead of position and momentum, Heisenberg's equation can also be
expressed in terms of energy and time. Again, the more constrained one variable
is, the less constrained theother is. It is thereforepossible that, for very, very short
periods of time, a quantumsystem's energycan behighly uncertain, somuch that
particles can appear out of the vacuum. These"virtualparticles" appear in pairs –
an electron and its antimatter pair, thepositron, say – for a short while and then
annihilateeach other. This is well within thelaws of quantum physics, as long as
the particles only exist fleetingly and disappear when their time is up.
Uncertainty,then, is nothing toworry about in quantum physics and, in fact, we
wouldn't be here if this principle didn't exist.
Energy Levels of Electrons
As you may remember from chemistry, an atom consists of electrons orbiting
around a nucleus. However, the electrons cannot choose any orbit they wish.
They arerestricted toorbits with only certain energies. Electrons can jump from

6. one energy level to another, but they can never have orbits with energies other
than the allowed energy levels.
Let's look at the simplest atom, a neutral hydrogen atom. Its energy levels are
given in the diagram below. The x-axis shows the allowed energy levels of
electrons in a hydrogen atom, numbered from 1 to 5. The y-axis shows each
level's energy in electron volts (eV). One electron volt is the energy that an
electron gains when it travels through a potential difference of one volt (1 eV =
1.6 x 10-19
Joules).
Electrons in a hydrogen atom must be in one of the allowed energy levels. If an
electron is in thefirst energy level, it must have exactly -13.6 eV of energy. If it is
in the second energy level, it must have -3.4 eV of energy. An electron in a
hydrogen atom cannot have -9 eV, -8 eV or any other value in between.
Let's say the electron wants to jump from the first energy level, n = 1, to the
second energy level n = 2. The second energy level has higher energy than the

7. first, so to move from n = 1 to n = 2, the electron needs to gain energy. It needs to
gain (-3.4) - (-13.6) = 10.2 eV of energy to makeit up to the second energy level.
The electron can gain theenergy it needs by absorbing light. If theelectron jumps
from thesecond energy level down to the first energy level, it must give off some
energy by emitting light. The atom absorbs or emits light in discrete packets
called photons, and each photon has a definite energy. Only a photon with an
energy of exactly 10.2 eV can be absorbed or emitted when the electron jumps
between the n = 1 and n = 2 energy levels.
The energy that a photon carries depends on its wavelength. Since the photons
absorbed or emitted by electrons jumping between the n = 1 and n = 2 energy
levels must have exactly 10.2 eV of energy, the light absorbed or emitted must
have a definite wavelength. This wavelength can be found from the equation
E = hc/l,
where E is theenergy of the photon (in eV), h is Planck's constant(4.14 x 10-15
eV
s) and c is the speed of light (3 x 108
m/s). Rearranging this equation to find the
wavelength gives
l = hc/E.
A photon with an energy of 10.2 eV has a wavelength of 1.21 x 10-7
m, in the
ultraviolet part of thespectrum. Sowhen an electron wants to jump fromn = 1 to
n = 2, it must absorb a photon of ultraviolet light. When an electron drops from n
= 2 to n = 1, it emits a photon of ultraviolet light.
The step from the second energy level to the third is much smaller. It takes only
1.89 eV of energy for this jump. It takes even less energy to jump from the third
energy level to the fourth, and even less from the fourth to the fifth.

8. What would happen if the electron gained enough energy to make it all the way
to 0eV? The electron would then be free of the hydrogen atom. The atom would
be missing an electron, and would become a hydrogen ion.
The table below shows the first five energy
levels of a hydrogen atom.
Energy Level Energy
1 -13.6 eV
2 -3.4 eV
3 -1.51 eV
4 -.85 eV
5 -.54 eV
You can use this method to find the wavelengths emitted by electrons jumping
between energy levels in various elements. However, finding the correct energy
levels gets much more difficult for larger atoms with many electrons. In fact, the
energy levels of neutral helium are different from the energy levels of singly
ionized helium! Therefore, we will skip how to calculate all the energy levels for
different atoms for now. The energy levels are published in the CRC Handbook of
Chemistry and Physics if you want to look them up.
Atomic Spectra
All condensed matter (solids, liquids, and dense gases) emit electromagnetic
radiationat all temperatures.Also, this radiation has a continuous distribution of

9. several wavelengths with different intensities. This is caused by
oscillatingatoms andmolecules andtheirinteraction with the neighbours. In the
early nineteenthcentury, it was established that each element is associated with a
characteristicspectrumof radiation, knownas Atomic Spectra.Hence, thissuggests
an intimate relationship between the internal structure of an atom and the
spectrum emitted by it.
When an atomic gas or vapouris excitedunder lowpressureby passing an electric
currentthroughit, thespectrumof theemitted radiationhas specific wavelengths.
It is important to note that, such a spectrum consists of bright lines on a dark
background. Thisis an emission linespectrum.Hereis an emission linespectrumof
hydrogen gas:
Theemission linespectra workas a ‘fingerprint’ for identification of the gas. Also,
on passing a whitelight through the gas, the transmitted light shows some dark
lines in thespectrum.Theselines correspondtothosewavelengths thatarefound in
the emission line spectra of the gas. This is the absorption spectrum of
the material of the gas.
Types of spectra

10. When white light falls on a prism, placed in a spectrometer, the waves of
different wavelengths aredeviated to different directions by theprism. The image
obtained in the field of view of the telescope consists of a number of coloured
images of the slit. Such an image is called a spectrum.
If the slit is illuminated with light from sodium vapour lamp, two images of
the slit are obtained in the yellow region of the spectrum. These images are the
emission lines of sodium having wave lengths 5896Ao and 5890Ao. This is
known as spectrum of sodium.
The spectra obtained fromdifferent bodies can be classified intotwo types (i)
emission spectra and (ii) absorption spectra.
(i) Emission spectra
When the light emitted directly from a source is examined with a
spectrometer, the emission spectrum is obtained. Every source has its own
characteristic emission spectrum.
The emission spectrum is of three types.
1. Continuous spectrum
2. Line spectrum and
3. Band spectrum
1. Continuous spectrum

11. It consists of unbroken luminous bands of all wavelengths containing all the
colours from violet to red. These spectra depend only on the temperature of
the source and is independent of the characteristic of the source.
Incandescent solids, liquids, Carbon arc, electric filament lamps etc, give
continuous spectra.
2. Line spectrum
Line spectra aresharp lines of definite wavelengths. It is the characteristic of
the emitting substance. It is used to identify the gas.
Atoms in the gaseous state, i.e. free excited atoms emit line spectrum. The
substancein atomic statesuch as sodium in sodium vapour lamp, mercury in
mercury vapour lamp and gases in discharge tube give line spectra (Fig. 5.4).
3. Band Spectrum
It consists of a number of bright bands with a sharp edge at one end but
fading out at the other end.

12. Band spectra are obtained from molecules. It is the characteristic of the
molecule. Calcium or Barium salts in a bunsen flame and gases like carbon-
di-oxide, ammonia and nitrogen in molecular statein the discharge tube give
band spectra. When the bands are examined with high resolving power
spectrometer, each band is found to be made of a large number of fine lines,
very close to each other at the sharp edge but spaced out at the other end.
Using band spectra the molecular structure of the substance can be studied.
(ii) Absorption Spectra
When the light emitted from a sourceis made to pass through an absorbing
materialand then examined with a spectrometer, theobtained spectrum is called
absorption spectrum. It is the characteristic of the absorbing substance.
Absorption spectra is also of three types
1. continuous absorption spectrum
2. line absorption spectrum and
3. band absorption spectrum

13. 1.Continuous absorption spectrum
A pure green glass plate when placed in the path of white light, absorbs
everything except green and gives continuous absorption spectrum.
2.Line absorption spectrum
When light from the carbon arc is made to pass through sodium vapour and
then examined by a spectrometer, a continuous spectrum of carbon arc with
two dark lines in the yellow region is obtained as shown in Fig.5.5.
3. Band absorption spectrum
If white light is allowed to pass through iodine vapour or dilute solution of
blood or chlorophyll or through certain solutions of organic and inorganic
compounds, dark bands on continuous bright background are obtained. The
band absorption spectra are used for making dyes.

14. Spectral Series of Atomic Spectra
Normally, onewould expect to find a regular pattern in the frequencies of light
emitted by a particular element.Let’slook at hydrogenas an example. Interestingly,
at thefirst glance,it is difficult tofind anyregularityor order in theatomicspectra.
However, on closeobservation, it canbeseen that thespacingbetween lines within
certainsets decreases in a regular manner. Each of these sets is a spectral series.
Five spectral series identified in hydrogen are
1. Balmer Series
2. Lyman Series
3. Paschen Series
4. Brackett Series
5. Pfund Series
Further, let’s look at the Balmer series in detail.
Balmer Series

15. In 1885, whenJohannBalmerobserveda spectralseries in the visible spectrum of
hydrogen, he made the following observations:
 The longest wavelength is 656.3 nm
 The second longest wavelength is 486.1 nm
 And the third is 434.1 nm
 Also, as thewavelength decreases the lines appear closer together and weak
in intensity
 He found a simple formula for the observed wavelengths:
Further,for n=∞, you canget the limit of the series at a wavelength of 364.6 nm.
Also, you can’t see any lines beyond this; only a faint continuous

16. spectrum.Furthermore, like the Balmer’s formula, here are the formulae for the
other series:
Lyman Series
Paschen Series
Brackett Series
Pfund Series