Solid state physics, lattice constants, ionic radii, nacl

In summary, the three compounds NaCl, NaBr, and KCl all have the same NaCl structure. Using the given lattice parameters and the assumption that the spacings are determined by the ionic radii, the expected value for the lattice constant of KBr is 6.64A°, which is obtained by doubling the sum of the calculated radii for K+ and Br-. Additionally, the radii of Cl-, Br-, and K+ are found to be 1.85A°, 2.02A°, and 1.30A° respectively. The lattice parameter for KBr can also be calculated using the distance between the nearest positive and negative ions, which is approximately equal to the sum of
  • #1
izzy93
35
0

Homework Statement



NaCl (a0 = 5.64A° ), NaBr (a0 = 5.98A° ) and KCl (a0 = 6.30A° ) all have the same structure, which
is the NaCl structure.

(a) Assuming the spacings are determined by the ionic radii of the relevant ions, what would value
would you expect for the lattice constant of KBr?
(b) If the Na+ ion has a radius of 0.97A° , determine the radii of the other ions.


Homework Equations



lattice constant for nacl type structure =2cl-radius + 2 na+ radius ??

The Attempt at a Solution



a, I used the interionic distance of NaBr= 5.98A°/2 = 2.99A°

and then pythagorous to finde the diameter of Br- =4.228A°

do the same with KCl, I got the cl- diameter to be 4.455A°

and then as the lattice parameter = the length of one side of the cubic structure;
2cl-radius + 2 k+ radius = 6.30A°
k+ radius =0.9225A°

therefore the lattice constant of kbr = 2(0.9225A°) + 2(4.228/2) = 6.07 A°

The answer given is 6.64 A°. Is there another way to do this or have I got the definition of the lattice parameter entirely wrong?

b, got this part right r_Cl:1.85A° r_Br:2.02A° r_K:1.30A°

Any help would be much appreciated
 
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  • #2
izzy93 said:

Homework Statement



NaCl (a0 = 5.64A° ), NaBr (a0 = 5.98A° ) and KCl (a0 = 6.30A° ) all have the same structure, which
is the NaCl structure.

(a) Assuming the spacings are determined by the ionic radii of the relevant ions, what would value
would you expect for the lattice constant of KBr?
(b) If the Na+ ion has a radius of 0.97A° , determine the radii of the other ions.

Homework Equations



lattice constant for nacl type structure =2cl-radius + 2 na+ radius ??

The Attempt at a Solution



a, I used the interionic distance of NaBr= 5.98A°/2 = 2.99A°

and then pythagorous to finde the diameter of Br- =4.228A°

do the same with KCl, I got the cl- diameter to be 4.455A°

and then as the lattice parameter = the length of one side of the cubic structure;
2cl-radius + 2 k+ radius = 6.30A°
k+ radius =0.9225A°

therefore the lattice constant of kbr = 2(0.9225A°) + 2(4.228/2) = 6.07 A°

The answer given is 6.64 A°. Is there another way to do this or have I got the definition of the lattice parameter entirely wrong?

b, got this part right r_Cl:1.85A° r_Br:2.02A° r_K:1.30A°

Any help would be much appreciated

The distance between the nearest positive and negative ions is approximately equal to the sum of the ionic radii, but the distance between the negative ions, a0/√2 is not quite equal to their diameter. See picture. The opposite can be also true, in case of big negative ions they touch each other, but the positive ions do not touch the negative ones. Use only the lattice parameters and the given radius of the Na ion to get the radii of the other ions and the lattice parameter of KBr. You got rK and rBr: the lattice parameter of KBr is equal to twice the sum of these radii.

ehild
 

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FAQ: Solid state physics, lattice constants, ionic radii, nacl

1. What is solid state physics?

Solid state physics is a branch of physics that deals with the physical properties of solid materials, especially the behavior of electrons and atoms in solids.

2. What is a lattice constant?

A lattice constant is the distance between the atoms in a crystal lattice. It is a fundamental property that determines the overall structure and properties of a solid material.

3. What are ionic radii?

Ionic radii are the distance from the nucleus to the outermost electron in an ion. They are used to describe the size of an ion and play a crucial role in determining the structure and properties of ionic compounds.

4. How are lattice constants and ionic radii related?

Lattice constants and ionic radii are closely related as they both determine the overall structure and properties of a solid material. The size of the ions and the distance between them, represented by the lattice constant, will affect the strength of the ionic bond and the resulting properties of the material.

5. How does NaCl demonstrate the relationship between lattice constants and ionic radii?

Sodium chloride (NaCl) is a common example used to illustrate the relationship between lattice constants and ionic radii. The small size of the sodium ion and the larger size of the chloride ion result in a crystal lattice with a specific lattice constant, which gives NaCl its characteristic properties such as high melting point and solubility in water.

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