<< Chapter < Page Chapter >> Page >
A pair of images is shown that has four sections. In the first section, two sinusoidal waves are shown, one drawn above the other, and a section from the top of one curve to the top of the next curve is labeled “lambda.” The curves align with one another. The phrase below this reads “Constructive interference.” A right facing arrow leads from the first section to the second, which shows one larger sinusoidal curve that has higher and lower peaks and troughs. A section from the top of one curve to the top of the next curve is labeled “lambda” and the phrase below this reads “Maxima and minima reinforce.” In the second section, two sinusoidal waves are shown, one drawn above the other, and a section from the top of one curve to the top of the next curve is labeled “lambda.” The curves do not align with one another. The phrase below this reads “Destructive interference.” A right facing arrow leads from the first section to the second, which shows one flat line. The phrase below this reads “Maxima and minima cancel.”
Light waves occupying the same space experience interference, combining to yield waves of greater (a) or lesser (b) intensity, depending upon the separation of their maxima and minima.

When X-rays of a certain wavelength, λ , are scattered by atoms in adjacent crystal planes separated by a distance, d , they may undergo constructive interference when the difference between the distances traveled by the two waves prior to their combination is an integer factor, n , of the wavelength. This condition is satisfied when the angle of the diffracted beam, θ , is related to the wavelength and interatomic distance by the equation:

n λ = 2 d sin θ

This relation is known as the Bragg equation    in honor of W. H. Bragg , the English physicist who first explained this phenomenon. [link] illustrates two examples of diffracted waves from the same two crystal planes. The figure on the left depicts waves diffracted at the Bragg angle, resulting in constructive interference, while that on the right shows diffraction and a different angle that does not satisfy the Bragg condition, resulting in destructive interference.

Two similar figures are shown. The first figure, labeled “Constructive Interference,” shows two horizontal rows of seven black dots with a line passing through them. The fourth dots of each row have a vertical line connecting them. The distance between these rows is labeled “d.” A beam labeled “Incident beam” descends at an angle labeled “theta” until it hits the line connecting the fourth dots, after which a diffracted beam ascends at the same angle “theta.” A dotted line is drawn across the diffracted beam. The second figure, labeled “Destructive interference,” is very similar, except that the angles “theta” are far more acute, making the slopes of the beams more shallow.
The diffraction of X-rays scattered by the atoms within a crystal permits the determination of the distance between the atoms. The top image depicts constructive interference between two scattered waves and a resultant diffracted wave of high intensity. The bottom image depicts destructive interference and a low intensity diffracted wave.

An X-ray diffractometer, such as the one illustrated in [link] , may be used to measure the angles at which X-rays are diffracted when interacting with a crystal as described earlier. From such measurements, the Bragg equation may be used to compute distances between atoms as demonstrated in the following example exercise.

A diagram, labeled “a” shows a cube on the left with a channel bored into its right side labeled “X dash ray source.” A beam is leaving from this channel and traveling in a horizontal line toward an oval-shaped, short tube, labeled “Collimator to focus beam” and “X dash ray diffraction,” where it passes through a cube labeled “Crystalline material” and scatters onto a vertical sheet labeled “Imaging surface.” A second diagram, labeled “b,” shows a square sheet with a large dot in the center labeled “X dash ray beam,” that is surrounded by smaller dots arranged in rings and labeled “Diffracted X dash rays.”
(a) In a diffractometer, a beam of X-rays strikes a crystalline material, producing (b) an X-ray diffraction pattern that can be analyzed to determine the crystal structure.

Using the bragg equation

In a diffractometer, X-rays with a wavelength of 0.1315 nm were used to produce a diffraction pattern for copper. The first order diffraction ( n = 1) occurred at an angle θ = 25.25°. Determine the spacing between the diffracting planes in copper.

Solution

The distance between the planes is found by solving the Bragg equation, = 2 d sin θ , for d .

This gives: d = n λ 2 sin θ = 1 ( 0.1315 nm ) 2 sin ( 25.25 ° ) = 0.154 nm

Check your learning

A crystal with spacing between planes equal to 0.394 nm diffracts X-rays with a wavelength of 0.147 nm. What is the angle for the first order diffraction?

Answer:

21.9°.

Got questions? Get instant answers now!

X-ray crystallographer rosalind franklin

The discovery of the structure of DNA in 1953 by Francis Crick and James Watson is one of the great achievements in the history of science. They were awarded the 1962 Nobel Prize in Physiology or Medicine, along with Maurice Wilkins , who provided experimental proof of DNA’s structure. British chemist Rosalind Franklin made invaluable contributions to this monumental achievement through her work in measuring X-ray diffraction images of DNA. Early in her career, Franklin’s research on the structure of coals proved helpful to the British war effort. After shifting her focus to biological systems in the early 1950s, Franklin and doctoral student Raymond Gosling discovered that DNA consists of two forms: a long, thin fiber formed when wet (type “B”) and a short, wide fiber formed when dried (type “A”). Her X-ray diffraction images of DNA ( [link] ) provided the crucial information that allowed Watson and Crick to confirm that DNA forms a double helix, and to determine details of its size and structure. Franklin also conducted pioneering research on viruses and the RNA that contains their genetic information, uncovering new information that radically changed the body of knowledge in the field. After developing ovarian cancer, Franklin continued to work until her death in 1958 at age 37. Among many posthumous recognitions of her work, the Chicago Medical School of Finch University of Health Sciences changed its name to the Rosalind Franklin University of Medicine and Science in 2004, and adopted an image of her famous X-ray diffraction image of DNA as its official university logo.

An image shows a circular illustration with rings of dots that are blurred together.
This illustration shows an X-ray diffraction image similar to the one Franklin found in her research. (credit: National Institutes of Health)

Questions & Answers

What is rightful definition of element
angela Reply
an element is the group of (vertical columns) of the periodic table exhibit similar chemical behaviour.
Barnabas
okay
angela
is alkanes a saturated hydrocarbon?
Faith Reply
yup
Oladayo
it's saturated cos it has single bonds
Oladayo
yh....because they don't undergo additional reactions which hydrogen and other atoms can add across the carbon-carbon or triple bond
patience
and me...I'm I wrong?
patience
how does metal looses electron
Sammy Reply
By oxidation and reduction
hamidat
by oxidation loss
Official
An acid is a proton donor.
Eric Reply
what is an acid
Amara Reply
an acid is a substance when dissolved in water produces hydrogen ion or hydroxonium ion
hamidat
good
Mudassir
thanks
hamidat
is a substance which dissolves in water to produce hydrogen ions as the only positively charged ions
Kwagala
what is ionic bonding
Kylian Reply
It involves the transferring of electron from a metal to a non mental
hamidat
that's right
Edward
bonding between a metal and a non metal
miriam
calculate the hydrogen ion concentration of the solution when pH=5
Adamu Reply
answer pls
Adamu
no ideas
hamidat
What is thermodynamics
prince Reply
what is the meaning this word twentieth
dhu
Is the branch of physics that deal with heat and temperature and their relation to work, energy and properties of matter
Edward
There are no topics on hydrocarbons
Zina Reply
I don't understand
hamidat
they are there please check under organic chemistry in the contents.
Kwagala
its not making sense to me I still don't understand
megan Reply
How and why
Betrice
yes
megan
we need diagram for easy going and understand
serah
How can we easily differentiate between the 5 gas laws
Favour Reply
first amd foremist me i only know 3 gas laws, so please list them here
Kwagala
the gas laws i know include pressure law boyles law charles law i differentiate these with this formular big take classy pork pigs. viral i read thus as 1 big classy pigs take pork viral big.....take means in boyles law,temp is constant clasy.....prk mns in chrls lw, press cons
Kwagala
classy.....pork means in charles law pressure is constant pigs.....viral means, in pressure law volume is kept constsng ,the rest is the same boyles states that vol of a gas is inversely prop to volume keeping temp constant charles law, state vol of a gas is directly prop to temp keepn pressure cns
Kwagala
how many carbon is present in alkene
Alase Reply
it's the carbon to carbon being double bonded to each other that makes it an alkene, not the amount of carbon itself. ex: C=C, C=C=C. both are alkenes.
Phill
I need more light on alkene
chidera
an alkene is a hydrocarbon, you can find this under the sub topic of organic chemistry in this textbook, check it out please,but before you know about alkenes you should first know about alkanes, alkanes are saturated and dnt easily react while alkenes have double bonds and can react .
Kwagala
other usefullness of hydrogen apart from this, it is colourless, odourless and tasteless
Bukunmi Reply
it is neutral to litmus paper, it is insoluble in water
hamidat
the enthalpy of a system
Nasirat Reply
changing in heat of a system which can be lost or gained
Yussuf
is the energy change that occurs when molar quantities of reactants as stated in a chemical equation completely react
Kwagala
enthalpy of reaction is the energy change that occurs when molar quantities of reactants as stated in a chemical equation completely react
Kwagala
what is the unit of pressure
Tim Reply
what is pressure measured in?
Tim
Pascal
Stupid
millimeter mercury ,mmHg or ATM
hamidat
it is atm...in lower case not upper
Kwagala

Get the best Chemistry course in your pocket!





Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Chemistry' conversation and receive update notifications?

Ask