5

The unit cell in a crystal of diamond belongs to a crystal system different from any we have discussed. The volume of a unit cell of diamond is $0.0454 mathrm{~nm}^...

Question

The unit cell in a crystal of diamond belongs to a crystal system different from any we have discussed. The volume of a unit cell of diamond is $0.0454 mathrm{~nm}^{3}$ and the density of diamond is $3.52 mathrm{~g} / mathrm{cm}^{3}$. Find the number of carbon atoms in a unit cell of diamond.

The unit cell in a crystal of diamond belongs to a crystal system different from any we have discussed. The volume of a unit cell of diamond is $0.0454 mathrm{~nm}^{3}$ and the density of diamond is $3.52 mathrm{~g} / mathrm{cm}^{3}$. Find the number of carbon atoms in a unit cell of diamond.



Answers

Platinum crystallizes with the face-centered cubic unit cell. Theradius of a platinum atom is 139 pm. Calculate the edge length of the unit cell and the density of platinum in g/cm3.

So you were given some information about Diamond and it's unit so and we want to use the information given to find the number of carbon atoms per unit. So So they tell us that the volume is 0.454 cubic nanometers. And if we take that value, I wanted to emphasize that this is actually Purcell. So I wrote in Purcell, that'll make a lot more sense in a second, and then density is equal to 3.52 grams per cubic centimeter. So the reason I always write out the full units on these problems is because where we want to get is a number with the units Adam's Purcell. And if we know the conversion factors that we're starting with, and we know the conversion factor that we want to get to, it makes it a lot easier to manipulate these numbers. So what I would recommend doing is we'll start with the density first, so we have 3.52 grams per cubic centimeter, and we're basically just gonna go through several steps to get from grams per cubic centimeter. It's Adam's for so do you. Neither do that, starting with the top. You can do it, starting with the bottom. I choose to go with the top for this problem. So if I want to go from Graham's toe Adams, I need to go through moles and then I've got his number. So one more of, um, diamond. So it's made up of carbon atoms. So it's just gonna be the Moler massive carbon point of one girl's role. We're gonna put in our big Odgers number 6102 to tend to the 23rd Adam's promote. When we do that, we were able to cancel out our units and now we have Adam's in the numerator. So we're already most of the way towards getting to this final answer and Adam's for So So we already know what the volume Purcell is. The volume Purcell was given to us and Nana meters cubic Nana meters. So the first thing that we should probably dio is either convert that to cubic centimeters or throwing the conversion factor for cubic centimeters. Two cubic centimeters. I actually chose to do it that way so you can go through a math yourself. The conversion factor for these is there One times 10 to the negative 24th 1st cubic centimeters per cubic centimeter and then finally running out of space here. But if we continue this line down to the bottom and then multiply what we have, bye the density of the volume that we were given, we can now go through and use this centimeter to cancel this centimeter and these animators to cancel these Nana meters and then multiply the top of the fraction all the way across and the denominator all the way across. And that's where we end up finding that the the real answer comes out to be about 8.1 Realistically, you have to have a whole number of atoms per so and we have about eight Adam's poor unit cell in diamond.

Okay, So for this question, they tell us the radius of platinum is 139 pickle meters, and they want us to calculate the edge linked of the units. So Andy density. So the first thing that we have to do is calculate how much? One atom of platinum ways. So, Adam, right? So are we going to do is take the molar mass of one mole of platinum, and that is 195 0.64 g. We take that. That's one more time, and we can use discovers in one mo. And when an ah is equal to six points 02 two times 10 20 23rd. Adams. Right. That's all the goggles number. So one mole of any ah element as you go to 6.22 times sensor, 23rd Adams. We plucked out into de caca. We get 3.239 times 10 30 22 g. So that's how much one platinum Adam ways so. But the thing is, there are four atoms present in the unit cell of platinum because they tell us that platinum crystallizes with the face centre cubic units. L so face centred cubic units. L means that at each corner of the Cube there are one platinum Adam. And then there are one platinum Adam on each face of the cube. So since there are eight on each corner of the Q and each corner each Adam on the corner is only 18 inside. That's one right. And there sits on the surface and each surface. Adam is half inside last three and three plus one export. So I'm gonna take this number and multiply it by four. And we get 1 to 9 56 1.2956 times, 10 times 10. Trudy Negative. 21. Right. So that is the mass of the unit. So, uh, now we can save this value for later. So for part A, they're telling us to calculate D ed joins, right? So they tell us to Your radius of platinum is 139 PICO meters. So we can just use this ah, formula Right here. Length is equal to two square root of two times that by our right. So choose gravel of two times and by our 139 pickle meters. But we have to convert this Ah pickle meters into, actually, uh, after we can keep it as a PICO meter. Right. We put that into the calculate. We get length as you go to 393 p computers. Careful, Part B. They want us to calculate density. So what we have to do now is, since they want the answer in grams per setting, there's Cube. Were the convert this PICO meters into centimeters. Right. Okay, so we have 393 pick a meters. The conversion is one centimeter is equal to one times 10 to the negative. 10. He commuters. All right, put that into the calculator and we get 3.93 times 10 to the negative eight centimeters. Now, what we're gonna do is find volume. So we have the length of each side and centimeters. So 3.93 times 10 to the negative. Eight centimeters. Right? Volume is this is the cube. All sides are insanely. So we just got a cute this after we cute that we should get 60.698 times 10 sooty negative, 24 centimeters cube. Okay, so they want the density and grams per centimeters cube. Right. So we have Centimeters Cube, and we also have grams right here. So all we gotta do is take the two values and we just divide them. So, density does he go to mass? Divided by volume. So 129 points? Uh, not 129. It's 1.29 56 years, 1.2956 times, 10 to the negative. 21 over 60.698 times, 10 to the negative. 24 and we get 21 0.3 grams per centimeters cube.

Eso for this question. They tell us to you. Radius is 142 pickle meters and they want us to calculate the volume of the face centre. Cubic units. So in Centimeters Cube, right? So the first thing that we can do is let's just convert the PICO meters into centimeters so that we don't have to cover at the end. So 142 p commuters see conversion between P commuters and centimeters is that one peak. A meter is equal to one times 10 to the negative 10 centimeters. We put that into detach later and we should get 1.42 times 10 to the negative eight centimeters as our answer Now, in order to find the length of each side of the cube, since we're working with a face center, que do you feel ain't as equal to square roots of eight times are or ah, go right to gurgle of two times are it doesn't matter which one. So I'm just gonna use two times grew of two is times it by our and we know the R is 1.42 times tens and negative eight so 1.42 times 10 3 negative centimeters. So put that into the tackle it and we can't 4.16 times 10 to the negative eight centimeters and they want the volume, right? So volume since we're working with the Cube, every edge of the cube are the same length and volume insulin time, four times hike. And since there is the same length, you can just take the length and a cubit, right so length Q. Is you go to a volume which is people to ah 4.16 times 10 to the negative eight centimeters. Ah, Cube. We get 6.48 times 10 to the negative 20 23 centimetres cute.

Okay, So for this question, the first thing that we should do is calculate the mass of a rhodium Adam. So we know the molar mass of Rodion. One mole of rhodium is equal to 102.9 g. Right? That's one mold. And we know that we can determine the massive one Adam by using the Al Godhra number. So one mo is equal to six point. Oh, too true times 10 to the 23rd Adams. So 23rd, Adams. All right, plug that into a D calculated. And we get 1.7087 times, 10 to the negative. 22 grams Now. Ah, for this we're working with a face centre. Cubic units sell. This means that there are four atoms present, right for a face centre. Cubic self. There are a Adams one on each, uh, corner of the cube. And since each Adam on the corner cube is only 18 inside the you price, so a Adams one agents are the cue. That is one. And then there is also six Adams. One on each face is empty. Adams on each face are only half inside the cube. So we get three by so three plus one is four. So we get four Adams. So we have to multiply this number by four. And we get actually, let's do four times A by 1.7087 times 10 to the negative. 22 right to get 6.8348 times 10 to the negative. 23rd as r. Graham. So the mass. Okay, so we have the mass and we know d density. So we can use that to determine volume. So mass is equal to ah. Now density is equal to density is you go to mass divided by volume, right? So in order saw for volume are we gonna do is multiply both sides by volume and then divide both sides by Dempsey. So we get volume is equal to mass divided by identity, Right, So we can do now is plug these numbers. And so volume is able to the mass which we determined to be six points 8348 times 10 to so just 33 for eight times sensory negative, 23rd And the density They said it was 12.41 So 12.41 g per centimeters cube. And we should get five points over No, five points, 507 times 10 to the negative. 23rd centimeters Cube. Right. So we have volume. Now we have to tell me what the link is. So the length of a cube is the que Grew up the volume, right? Because each weight of a cube is the same length. So it we cue the length weekend volume. So we have the cube root the volume, so ah, length is equal to the cube root of 5.507 times 10 to the negative 2030 centimeters cube. And we get the answer to be 3.805 times 10 to the negative H centimeters. Well, we got the lane. So what is three You, uh, formula for the length of a face centred. Cubic Youness el we'll link is equal to two times square of two times. And I are right and we want radius. We have the length so we can determine what the radius is just by dividing both sides by two ah times grew of to write. This cancels out so radius Ah, after we plug in our value radius is equal to 3.805 times 10 to the negative. 80 centimeters. Oh, virtues girl of to And we get 1.345 times 10 to the negative. Eight centimeters now, depending on what they want. The answer in if they want it in Pekka meters. Well, are you gonna do it? Take 1.3 45 times. It by times tends to native eight centimeters and then you use this conversion. So one times 10 to the negative 10 Pekka meters is you go to one centimeter and you get 134.5 p commuters.


Similar Solved Questions

5 answers
First, find the total arclength, and then re-parameterize with respect to arclength thc following function: (cos? t,sin? t,cos(2t)), "/2 <t <t
First, find the total arclength, and then re-parameterize with respect to arclength thc following function: (cos? t,sin? t,cos(2t)), "/2 <t <t...
5 answers
Please show all steps,you are working at a lab that is trying to find the vaccine for COVID-19,and your boss assigns you the following numerical differentiation problem: using the derivative as well as the function construct a method that is Znd order with a quadratic error which approximates f' (a + b) which relies on f' (a), f(a) ad f(a + b) thank youl
Please show all steps,you are working at a lab that is trying to find the vaccine for COVID-19,and your boss assigns you the following numerical differentiation problem: using the derivative as well as the function construct a method that is Znd order with a quadratic error which approximates f'...
5 answers
Find the general solution of the given system of first order linear ODEs [3 Lz - Xj 4 X Ii 4 T- X24pLS)
Find the general solution of the given system of first order linear ODEs [3 Lz - Xj 4 X Ii 4 T- X2 4 pLS)...
5 answers
15. So far all of the numbers that Misty has found are a single statistic. Was knowing that Misty' $ sample was 58.3% male enough to infer that what she has been told is true? Is there a way we can help her feel more confident in her conclusions?
15. So far all of the numbers that Misty has found are a single statistic. Was knowing that Misty' $ sample was 58.3% male enough to infer that what she has been told is true? Is there a way we can help her feel more confident in her conclusions?...
5 answers
The distance from the lens of your eye to the retina (where the image is formed) is 2.5 cm. You can clearly see an object located 0.60 m from your eye. The focal length of your eye lens isSelect one; a.2.4 cm:b. 0.019 cm:c0.42 cm: d.52,5 cmThe density of wateris Tdoplkg lm} Approximate g as 10 Nlkg: One atmosphere (1 atm) is 100,000 Pa (Pa is N/m? IThe pressure dilference between the surface and depth in waterof 20 m isSelect one; a.0.2 atmb. 200,000 atrCatmd.2 ato
The distance from the lens of your eye to the retina (where the image is formed) is 2.5 cm. You can clearly see an object located 0.60 m from your eye. The focal length of your eye lens is Select one; a.2.4 cm: b. 0.019 cm: c0.42 cm: d.52,5 cm The density of wateris Tdoplkg lm} Approximate g as 10 N...
5 answers
22) Show all workl (2 pts) An airline estimates that 92% of people booked on their flights flight for which the maximum number actually show up. If the airline books 86 People on people who show up will crcen is 84 , what is the probability that the number capacity of the plane?
22) Show all workl (2 pts) An airline estimates that 92% of people booked on their flights flight for which the maximum number actually show up. If the airline books 86 People on people who show up will crcen is 84 , what is the probability that the number capacity of the plane?...
5 answers
Which statement correctly describes the 2 electrodes?The anode is positive and the cathode is negative The anode is negative and the cathode is positive The anode and cathode are both negative. The anode and cathode are both positive
Which statement correctly describes the 2 electrodes? The anode is positive and the cathode is negative The anode is negative and the cathode is positive The anode and cathode are both negative. The anode and cathode are both positive...
5 answers
Find the closest point to y in the subspace W spanned by V1 and V25y =V2 =2The closest point to y in W is the vector(Simplify your answers: _
Find the closest point to y in the subspace W spanned by V1 and V2 5 y = V2 = 2 The closest point to y in W is the vector (Simplify your answers: _...
5 answers
Question 21ptsWhat is the Ksp expression for Sr(OH)2 * 8HzO (8)?Kp-[Sr?*I[2OH] Ky-(Sr2"JIOHT? Kp-[Sr][OH:] Kp-[Sr-IIOH FIHzoji
Question 2 1pts What is the Ksp expression for Sr(OH)2 * 8HzO (8)? Kp-[Sr?*I[2OH] Ky-(Sr2"JIOHT? Kp-[Sr][OH:] Kp-[Sr-IIOH FIHzoji...
5 answers
What is the major product of the following reaction?CH,WatctCH;OHR-e-R ~CH;Mg BrRioCH,
What is the major product of the following reaction? CH, Watct CH;OH R-e-R ~CH;Mg Br Rio CH,...
5 answers
About 7% of the population has particular genetic mutation. 1000 people are randomly selected Find the mean for the number of people with the genetic mutation in such groups of 1000.
About 7% of the population has particular genetic mutation. 1000 people are randomly selected Find the mean for the number of people with the genetic mutation in such groups of 1000....
1 answers
A monoprotic acid HX has $K_{\mathrm{a}}=1.3 \times 10^{-3} .$ Calculate the equilibrium concentrations of $\mathrm{HX}$ and $\mathrm{H}_{3} \mathrm{O}^{+}$ and the $\mathrm{pH}$ for a $0.010 \mathrm{M}$ solution of the acid.
A monoprotic acid HX has $K_{\mathrm{a}}=1.3 \times 10^{-3} .$ Calculate the equilibrium concentrations of $\mathrm{HX}$ and $\mathrm{H}_{3} \mathrm{O}^{+}$ and the $\mathrm{pH}$ for a $0.010 \mathrm{M}$ solution of the acid....
5 answers
Find the complex Fourier series of the following function_ flz) =1, 2t < 1 2T _
Find the complex Fourier series of the following function_ flz) =1, 2t < 1 2T _...
5 answers
There are many positive concepts of health and safety that youhave read. Select any four positive concepts and discuss themthoroughly by highlighting one example in each case.
There are many positive concepts of health and safety that you have read. Select any four positive concepts and discuss them thoroughly by highlighting one example in each case....
5 answers
Problem 5A jar contains [2 colored balls _ There are red balls and blue balls _ Suppose draw replacement one-by- one Letballs withoutA be the event that the first ball drawn is red. B be the event that the second ball drawn red.What is P(BIA)? Are and B independent?
Problem 5 A jar contains [2 colored balls _ There are red balls and blue balls _ Suppose draw replacement one-by- one Let balls without A be the event that the first ball drawn is red. B be the event that the second ball drawn red. What is P(BIA)? Are and B independent?...
5 answers
The ' figure to the right : shows the electric field In a region of space In the BOTH the electric fileld strength at each ofthe space below; clearly rank four points (E1, E2, E3, E4) and the electric potential (V1, V2, V3, Va) at each of = the" four points Insert the appropriate symbols (<, >, =) below: Rank Electric Potentlal V:Rank Electric field E
The ' figure to the right : shows the electric field In a region of space In the BOTH the electric fileld strength at each ofthe space below; clearly rank four points (E1, E2, E3, E4) and the electric potential (V1, V2, V3, Va) at each of = the" four points Insert the appropriate symbols (...
5 answers
Let p(r) = 2V2. (a) Find the slope _ ofthe function's graph at v = 9 Slope 2(9) (6) Find an equation for rhe line tangent to the graph ofy (1,y) (9,6). P(z) at che poinc Tangent line: y To verify your results, make plot that includes the (I,y) (9,6) graph of y along with the graph ofthe P(z) near the point rangent line through that point:Submlt answer
Let p(r) = 2V2. (a) Find the slope _ ofthe function's graph at v = 9 Slope 2(9) (6) Find an equation for rhe line tangent to the graph ofy (1,y) (9,6). P(z) at che poinc Tangent line: y To verify your results, make plot that includes the (I,y) (9,6) graph of y along with the graph ofthe P(z) ne...
5 answers
(5) EVALvATE (25 Pts) (4) 5 42 dx (4 471+ V)T(6) (07" A~ () ( * eesGs> &, (14) S 7* (2) Sz4r(6) S4ppese {ep} 4 se*m6 Gk %*3 4-65(8) (IS Pts ) 5=z({ , 9 = 5(-}) Ten 0'5 6> Zk () 8< = ? (4) q = ? K71 K7i(1) Did You 4AvG Fyn Doing T4s Test? PlsG &yA4/N. (5rts) <nr
(5) EVALvATE (25 Pts) (4) 5 42 dx (4 471+ V) T (6) (07" A~ () ( * eesGs> &, (14) S 7* (2) Sz4r (6) S4ppese {ep} 4 se*m6 Gk %*3 4-65(8) (IS Pts ) 5=z({ , 9 = 5(-}) Ten 0'5 6> Zk () 8< = ? (4) q = ? K71 K7i (1) Did You 4AvG Fyn Doing T4s Test? PlsG &yA4/N. (5rts) <nr...
4 answers
Problem 2. Mass M= 0.500 kg is held at rest on a 50-degree incline plane, by a pushing force of magnitude F = 8.00 N applied parallel to the horizontal ground (see the fig: below) Let x-axis be along the incline, and y-axis perpendicular to the incline:Find the normal force n that the incline exerts on the block: Note: n # Mg; also n # Mg cos(0)2 Find static frictional force fs acting on the block to prevent it from moving up the incline plane. Note: fs # Usn
Problem 2. Mass M= 0.500 kg is held at rest on a 50-degree incline plane, by a pushing force of magnitude F = 8.00 N applied parallel to the horizontal ground (see the fig: below) Let x-axis be along the incline, and y-axis perpendicular to the incline: Find the normal force n that the incline exert...

-- 0.022241--