1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Yuliya22 [10]
3 years ago
6

(a) Compute the radius r of an impurity atom that will just fit into an FCC octahedral site in terms of the atomic radius R of t

he host atom (without introducing lattice strains). . (b) Repeat part (a) for the FCC tetrahedral site.

Chemistry
1 answer:
11Alexandr11 [23.1K]3 years ago
7 0

Answer:

a

The radius of an impurity atom occupying FCC octahedral site is 0.414{\rm{R}}

b

The radius of an impurity atom occupying FCC tetrahedral site is 0.225{\rm{R}} .

Explanation:

In order to get a better understanding of the solution we need to understand that the concept used to solve this question is based on the voids present in a unit cell. Looking at the fundamentals

An impurity atom in a unit cell occupies the void spaces. In FCC type of structure, there are two types of voids present. First, an octahedral void is a hole created when six spheres touch each other usually placed at the body center. On the other hand, a tetrahedral void is generated when four spheres touch each other and is placed along the body diagonal.

Step 1 of 2

(1)

The position of an atom that fits in the octahedral site with radius \left( r \right)is as shown in the first uploaded image.

In the above diagram, R is the radius of atom and a is the edge length of the unit cell.

The radius of the impurity is as follows:

2r=a-2R------(A)

The relation between radius of atom and edge length is calculated using Pythagoras Theorem is shown as follows:

Consider \Delta {\rm{XYZ}} as follows:

(XY)^ 2 =(YZ) ^2 +(XZ)^2

Substitute XY as{\rm{R}} + 2{\rm{R + R}} and {\rm{YZ}} as a and {\rm{ZX}} as a in above equation as follows:

(R+2R+R) ^2 =a ^2 +a^ 2\\16R ^2 =2a^ 2\\ a =2\sqrt{2R}

Substitute value of aa in equation (A) as follows:

r= \frac{2\sqrt{2}R -2R }{2} \\ =\sqrt{2} -1R\\ = 0.414R

The radius of an impurity atom occupying FCC octahedral site is 0.414{\rm{R}}

Note

An impure atom occupies the octahedral site, the relation between the radius of atom, edge length of unit cell and impure atom is calculated. The relation between the edge length and radius of atom is calculated using Pythagoras Theorem. This further enables in finding the radius of an impure atom.  

Step 2 of 2

(2)

The impure atom in FCC tetrahedral site is present at the body diagonal.

The position of an atom that fits in the octahedral site with radius rr is shown on the second uploaded image :

In the above diagram, R is the radius of atom and a is the edge length of the unit cell.

The body diagonal is represented by AD.

The relation between the radius of impurity, radius of atom and body diagonal is shown as follows:

AD=2R+2r----(B)

   In    \Delta {\rm{ABC}},

(AB) ^2 =(AC) ^2 +(BC) ^2

For calculation of AD, AB is determined using Pythagoras theorem.

Substitute {\rm{AC}} as a and {\rm{BC}} as a in above equation as follows:

(AB) ^2 =a ^2 +a ^2

AB= \sqrt{2a} ----(1)

Also,

AB=2R

Substitute value of 2{\rm{R}} for {\rm{AB}} in equation (1) as follows:

2R= \sqrt{2} aa = \sqrt{2} R

Therefore, the length of body diagonal is calculated using Pythagoras Theorem in \Delta {\rm{ABD}} as follows:

(AD) ^2 =(AB) ^2 +(BD)^2

Substitute {\rm{AB}} as \sqrt 2a   and {\rm{BD}} as a in above equation as follows:

(AD) ^2 =( \sqrt 2a) ^2 +(a) ^2 AD= \sqrt3a

For calculation of radius of an impure atom in FCC tetrahedral site,

Substitute value of AD in equation (B) as follows:

\sqrt 3a=2R+2r

Substitute a as \sqrt 2{\rm{R}} in above equation as follows:

( \sqrt3 )( \sqrt2 )R=2R+2r\\\\

r = \frac{2.4494R-2R}{2}\\

=0.2247R

\approx 0.225R

The radius of an impurity atom occupying FCC tetrahedral site is 0.225{\rm{R}} .

Note

An impure atom occupies the tetrahedral site, the relation between the radius of atom, edge length of unit cell and impure atom is calculated. The length of body diagonal is calculated using Pythagoras Theorem. The body diagonal is equal to the sum of the radii of two atoms. This helps in determining the relation between the radius of impure atom and radius of atom present in the unit cell.

You might be interested in
Which of these describes an ethical dilemma that drug designers could face?
LenKa [72]

The statement 'whether people should take medicine or if they should seek alternative treatments' describes an ethical dilemma that drug designers face.

<h3>What is drug development?</h3>

Drug development refers to all the processes from target drug identification to drug validation and commercialization.

Drug development involves different stages of development including preclinical and clinical trials.

Ethical dilemmas in drug development include the release of a drug that is ineffective when compared to parallel treatments.

Learn more about drug development here:

brainly.com/question/8187660

4 0
2 years ago
Hurry it’s for a test!! The arctic fox and gray wolf are two examples of
Lady_Fox [76]
B
Protect themselves from predators
4 0
3 years ago
Which compound 2-bromo-2-methylpropane or 2-chloro-2-methylpropane?
AURORKA [14]
The 2-bromo-1-chloro-2-methylpropane molecule contains a total of 14 atom(s). There are 4 Carbon atom(s), 8 Hydrogen atom(s), 1 Chlorine atom(s) and 1 Bromine atom(s). A chemical formula of 2-bromo-1-chloro-2-methylpropane can therefore be written as C4H8BrCl. Is it also commonly called as Propane.
6 0
3 years ago
Scientific endeavor must be driven by the needs of society and not by simple curiosity. true false
vazorg [7]
False people can do whatever they want without people telling them what to do.
5 0
3 years ago
How many moles of NaCl (s) can be formed from 32 moles of Cl2 (g) reacting with an excess of Na (s)?
blagie [28]

Answer:

64 moles

Explanation:

Let us begin by writing a balanced equation for the reaction. This is illustrated below:

2Na + Cl2 —> 2NaCl

From the equation above,

1 mole of Cl produced 2 moles of NaCl.

Therefore, 32 moles of Cl will produce = 32 x 2 = 64 moles of NaCl.

Therefore, 64 moles of NaCl are produced

7 0
3 years ago
Other questions:
  • Describe the reason why a reaction between two substances comes to an end.
    13·1 answer
  • A chemist has some 40% acid solution, some 60% acid solution, and a wholebunch of free time. How many liters of each should be u
    7·1 answer
  • Based on the kinetic theory, which statement is true?
    13·2 answers
  • When gases are treated as real, via use of the van der Waals equation, the actual volume occupied by gas molecules ________ the
    9·1 answer
  • I need help on this question
    15·2 answers
  • I just randomly remembered my 9 year old sister telling my 14 year old crush that he looks like and elf... she goes "You're like
    5·2 answers
  • Need a bf or gf fake or reallll<br> i dont care you can just take my points but .............. yea
    9·2 answers
  • If 8.500 g CH is burned and the heat produced from the burning is added to 5691 g of water at 21 °C, what is the final
    11·1 answer
  • The reaction responsible for producing the heat that maintains the temperature of your body is
    14·1 answer
  • Indicate whether each of the following gas liquid solid 1: the neon atoms in living display don't interact with other
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!