Which of the following materials may form crystalline solids? The energy transferred when an electron moves between electronic states is measured and is used to identify the types of atoms in a material. Your Ultimate AI Essay Writer & Assistant. Atomic packing : Signifies the way in which atoms are packed together. To perform this calculation, we need to know the volume of a cube and the volume of a sphere. The net potential energy between two adjacent ions, EN. So the total number of atoms in the cell is 3 + (1/2)2 + (1/6)62 = 6. ISBN 978-1-56032-992-3. Easiest way to remove 3/16" drive rivets from a lower screen door hinge? Miller indices are one of the most non-intuitive concepts most people encounter in an introductory course. First calculate the linear density for both directions in a FCC unit cell in terms of R (radius of Aluminum) and then circle the correct relationship. 2) You may not distribute or commercially exploit the content, especially on another website. Remember, you will not lose or gain any atoms in the structure. The unit cell for MgFe2O4 (MgO-Fe2O3) has cubic symmetry with a unit cell edge length of 0.836 nm. Atomic Structure (Freshman Chem.) Which principles of globalization did NR and his colleagues follow when, Prove that the mean and variance of the Poisson distribution during an, Determine the number of cycles per day and a production quantity per, Suppose you are now 40 years old and just accepted a new, K Dhoni is a business consultant.The following trial balance is provided at, A hypothetical AX type of ceramic material is known to have a, The unit cell for Cr2O3 has hexagonal symmetry with lattice parameters a. It is the fraction of volume in a crystal structure that is occupied by constituent particles. The latter is twice the distance between adjacent layers, i. e., twice the height of the regular tetrahedron whose vertices are occupied by (say) the central atom of the lower layer, two adjacent non-central atoms of the same layer, and one atom of the middle layer "resting" on the previous three. For example, in a fcc arrangement, a unit cell contains (8 corner atoms ) + (6 face atoms ) = 4 atoms. B-H vs M-H Hysteresis Loops: Magnetic Induction vs Magnetization (Similarities, Differences, and Points on the Graph), What is Scanning Electron Microscopy? Vatom = 4/3 PI (r)^3 Vlattice= a^3 OR (4r/ sqrt 2)^3, For Rocksalt structure APF: [4/3 *PI *((r)Na + (r)Cl)] / [(4 ((r)Na + (r)Cl))/ sqrt2]^3. (Simple Explanation), What are Space Groups? N LAA) APF = ; volume of unit cell 4 N 6.022 102 1cm 10'nm; Vsphere 120. Obviously, the edge of this tetrahedron is T%68?i`a'@>/f 5%44x l}Y%+00lgW:A1eQ( ` In crystallography, atomic packing factor (APF), packing efficiency, or packing fraction is the fraction of volume in a crystal structure that is occupied by constituent particles. Aluminum has an atomic radius of 0.1431 nm and a density of 2.71 g/cm3. One of your triangle legs will be the cubes side, . r Given that magnesium oxide (MgO) forms the pictured structure and in that structure the Mo and O ions are in contoct along the <100> family of directions, calculate the atomic packing factor (APF) and theoretical density (e) in lg/cm2]. engineering. Calculating the theoretical Density of a Lithium oxide, Calculating the Ionic strength of sodium acetylsalicylate. where is the volume of each type of atom. Princeton University Press. {\displaystyle {\sqrt {\tfrac {8}{3}}}a\ } Volume of the atoms divided by volume of the unit cell. In crystallography, atomic packing factor (APF), packing efficiency or packing fraction is the sum of the sphere volumes of all atoms within a unit cell (assuming the atomic hard-sphere model) divided by the unit cell volume. 1) You may use almost everything for non-commercial and educational use. is there a chinese version of ex. The size of the cube will be determined by the size of the atoms! How can the mass of an unstable composite particle become complex? The potential energy curves for the A-A and B-B bonds are compared. Connect and share knowledge within a single location that is structured and easy to search. If you projected the atom into one of those planes, it would be exactly in the middle of 3 atoms. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Module 5 Quiz Questions - Cell Bio, Module 6, Fundamentals of Engineering Economic Analysis, David Besanko, Mark Shanley, Scott Schaefer, Introduction to Chemical Engineering Thermodynamics, Hendrick Van Ness, J.M. We call this the planar density or area density. = Additionally, there is an atom in the middle of the cell. if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[320,100],'msestudent_com-netboard-2','ezslot_23',138,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-netboard-2-0');There are 3 atoms in the center, which fully contribute their volume to the unit cell. Does my formula look right otherwise? Show that the Schwarzschild radius for a star with mass equal to that of our Sun is 2.95 km. The focal length of the objective is +8.00cm+8.00 \mathrm{~cm}+8.00cm, and that of the eyepiece is 2.00cm-2.00 \mathrm{~cm}2.00cm. For multiple-component structures (such as with interstitial alloys), the APF can exceed 0.74. , and, therefore, Do NOT change the direction of axes. c rev2023.3.1.43269. ______ bonds are the only primary bonds that are directionally dependent. Search Textbook questions, tutors and Books, Change your search query and then try again, This problem asks us to compute the atomic packing factor for MgF. if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[120,600],'msestudent_com-netboard-1','ezslot_21',133,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-netboard-1-0');if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[120,600],'msestudent_com-netboard-1','ezslot_22',133,'0','1'])};__ez_fad_position('div-gpt-ad-msestudent_com-netboard-1-0_1'); .netboard-1-multi-133{border:none !important;display:block !important;float:none !important;line-height:0px;margin-bottom:15px !important;margin-left:auto !important;margin-right:auto !important;margin-top:15px !important;max-width:100% !important;min-height:600px;padding:0;text-align:center !important;}Imagine you had to pack spheres into a box. Atomic structure relates to the number of protons and neutrons in the nucleus of an atom, as well as the number and probability distributions of the constituent electrons. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties. APF = \frac{V_\text{atoms}}{V_\text{unit cell}} Luckily, its still relatively easy to visualize. Atomic packing factor(HCP lattice) In the Hexagonal unit cell, number of atoms = 12 corner atoms x 1/6 (shared by six unit cells) + Two face atoms x 1/2 + 3 interior = 6. Determine the relationship between linear density and elastic modulus. The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. If the density of this material is 4.52 g/cm3, compute its atomic packing factor. We hope, this article, Atomic Packing Factor APF, helps you. (Definition, Examples, and Metallurgy), The Difference Between Alloys and Composites (and Compounds), The Hume-Rothery Rules for Solid Solution. {\displaystyle a^{2}c\ } 2023 Copyright Materials Science & Engineering Student, link to Miller Indices for Crystal Directions and Planes, link to What Are Bravais Lattices? In FCC NaCl, there are 4 sodium ions and 4 chloride ions. For example, the elastic modulus along [001] if 70 GPa and along the [101] is 100 GPa. Usually, it makes the most sense to draw the unit cell so that a half-atom sticks out on both ends (like the red unit cell). U.S. Department of Energy, Material Science. In other words, the lattice will be larger than the basis. Indeed, three are the atoms in the middle layer (inside the prism); in addition, for the top and bottom layers (on the bases of the prism), the central atom is shared with the adjacent cell, and each of the six atoms at the vertices is shared with other six adjacent cells. I hope this is clear in the image below. It has a BCC structure, where the Ni atoms are located at the corners and the Cu atoms are located in the center of each cell. Simply find a crystallographically repeating area (the unit cell will always work) and divide that area by the area covered by the circles. Now, in terms of the radius, we can say that the volume of the cube is: Each atom is a sphere, so the volume per atom is: But, how many atoms do we have per unit cell? The volume of the atoms, and the volume of the unit cell. Once again, the pythagorean theorem saves the day! (How it Works, Applications, and Limitations), What is Materials Science and Engineering? (Definition, Types, Examples), Prince Ruperts Drops: The Exploding Glass Teardrop, Chemical Tempering (Chemically Strengthened Glass), 13 Reasons Why You Should Study Materials Science and Engineering. Lattice parameter is the height of the unit cell. Each corner atom would be shared between 6 other cells, so it contributes to each. Asking for help, clarification, or responding to other answers. Smith, Michael Abbott. $$. 5167 0 obj <> endobj Determine whether it has an FCC or a BCC crystal structure. Find the indicated scalar or vector. 2003-2023 Chegg Inc. All rights reserved. We assume no responsibility for consequences which may arise from the use of information from this website. Each side of the triangle has a length , so lets use that as our base. For example, metals with a high atomic packing factor will have a higher "workability" (malleability or ductility), similar to how a road is smoother when the stones are closer together, allowing metal atoms to slide past one another more easily. Introduction to the Thermodynamics of Materials (4th ed.). Youve learned how to calculate the lattice parameters and atomic packing fraction for simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) crystal systems. Atomic Packing Factor (APF) tells you what percent of an object is made of atoms vs empty space. It is then possible to calculate the APF as follows: On this Wikipedia the language links are at the top of the page across from the article title. 4 How many atoms or molecules are there in a mole of a substance? atom - electrons - 9.11 x 10-31 kg protons neutrons atomic number = # of protons in nucleus of atom = # of electrons of neutral species A [=] atomic mass unit = amu = 1/12 mass of 12C Atomic wt = wt of 6.023 x 1023 molecules or atoms 1 amu/atom = 1g/mol C 12.011 H 1.008 etc.} , then its height can be easily calculated to be Which of the following electron configuration is for an inert gas? What type(s) of bonding would be expected for brass (a copper-zinc alloy)? For a face-centered cubic unit cell, the number of atoms is four. a Yield Stress, Yield Strength, and Yield Point, Elasticity and Youngs Modulus (Theory, Examples, and Table of Values), True Stress-Strain vs Engineering Stress-Strain, Stress, Strain, and the Stress-Strain Curve, What Are Shape Memory Alloys? It is a dimensionless quantityand always less than unity. Hope you'll find our explanations and tips useful! @IvanNeretin I wasn't sure, thanks for clarifying that. Now we can plug into our first pythagorean theorem. Am not sure of my solutions, so solve these please. Which of the following best describes a epoxy? {\displaystyle c\ } Now we can make another triangle, between , , and . APF = \frac{2\pi(r_\ce{Cl}^3 + r_\ce{Na}^3)}{3(r_\ce{Cl} + r_\ce{Na})^3} As long as the line you draw is a valid representation of the overall crystal symmetry, any line will work! 2. Cesium chloride, perovskite, zinc blende, fluorite, rock salt, spinel. The atomic packing factor is defined as the ratio of sphere volume to the total unit cell volume, or APF = VS VC Since there are two spheres associated with each unit cell for BCC VS = 2(sphere volume) = 2 4R3 3 = 8R3 3 In metals there is usually only one atom, but in a ceramic, suppose there are 3 kinds of atoms: , , and . The only factor that can be used to predict crystal structure is the magnitude of the electrical charge of the ions. Do you need an answer to a question different from the above? Experts are tested by Chegg as specialists in their subject area. Which of the following bonds typically takes the most energy to break? Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. hbbd``b`$ &?w; Butterworth-Heinemann. Since were in 1-dimension, space means length. We can say that 1-dimensional packing is a linear density or line density. Then, the chemical formula of Lithium Oxide is, Given the ionic radii: Fe2+ = 0.074 nm and S2- = 0.184 nm, the crystal structure of FeS is similar to that of, Given the ionic radii: Na1+ = 0.102 nm and F1- = 0.133 nm, the crystal structure of NaF is similar to that of, Given the ionic radii: Mg2+ = 0.072 nm and O2- = 0.140 nm, the crystal structure of MgO is similar to that of, A hypothetical AX type ceramic material has density of 2.65 g/cc and cubic structure with edgle length of 0.43 nm. The expanded version would look like this: Additionally, atomic packing factor uses the hard sphere model. Mechanical Engineering questions and answers, 83. be its height. The coordination number for the cation, The structure of Lithium Oxide can be thought of as having anions in an FCC array with Lithium ions in all the tetrahedral positions. (Applications, History, and Metallurgy), Thermal Barrier Coatings (TBCs): Materials, Manufacturing Methods, and Applications, Hastelloy C-276 (Composition, Properties, and Applications), Magnetic Materials: Types of Magnetism, Applications, and Origin of Magnetism, Which Metals Are Magnetic? First, make a triangle with the body diagonal as the hypotenuse. We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. Since NaCl are one to one ratio as a compound, the coordination numbers of Na and Cl are equal. What types of subshell(s) does N shell contain? Miller Indices for Crystal Directions and Planes. {\displaystyle r^{3}\ } relatively high wear resistance, relatively high thermal insulation, relatively high hardness. If the density of this material is 4.52 g/cm3, compute its atomic packing factor. {\displaystyle a\ } By convention, the APF is determined by assuming that atoms . The elastic modulus is proportional to the density of the applied direction. Atomic mass is the mass of an individual atom, whereas atomic weight is the average (weighted) of the atomic masses of an atom's naturally occurring isotopes. A hypothetical metal has the BCC crystal structure, a density fo 7.24 g/cm^3, and an atomic weight of 48.9 g/mol. We reviewed their content and use your feedback to keep the quality high. However, its actually possible to define a smaller unit cell from the same atomic arrangement. For ceramic compound, what are the two characteristics of the component ions that determine the crystal structure? The unit cell is defined as the simplest repeating unit in a crystal. Crystal structure pertains to the arrangement of atoms in the crystalline solid material. For this computation, you will need to use ionic radii listed in Table12.3. And, since a few notation differences can completely change the meaning, advanced students What Are Bravais Lattices? Multiplying this area by the height gives. If the density of this material is 4.52 g/cm 3, compute its atomic packing factor. (List of Ferromagnetic and Ferrimagnetic Materials). Thanks for contributing an answer to Chemistry Stack Exchange! Harmony. An eyepiece consisting of a diverging lens intercepts the light before it comes to a focus and forms a virtual image at point BBB. Thermoset polymer (meaning that its shape cannot be reformed with elevated temperature.). $$, What you call a unit cell is actually 1/8 of it. Then, the ionic packing factor is, In the ceramic structure of PtO, the ionic radii are: Pt2+ = 0.052 nm and O2- = 0.132 nm. When determining the theoretical density of MgO, which of the following statements do you find are true? The hexagonal unit cell is just a hexagonal prism. 3 I take that the atomic packing factor is given by: What is the Difference Between Materials Science and Chemistry? Materials like Aluminum (FCC) are considered to have anisotropic properties. How to calculate the Atomic Packing Factor for face-centered cubic (FCC) and body-centered cubic (BCC) crystal structure.Atomic Packing Factor shows us that how closely the atoms are packed together in a unit cell. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Given that magnesium oxide (MgO) forms the pictured structure and in that structure the Mo and O ions are in contoct along the family of directions, calculate the atomic packing factor (APF) and theoretical density (e) in lg/cm2]. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Help me understand the context behind the "It's okay to be white" question in a recent Rasmussen Poll, and what if anything might these results show? An AX ceramic compound has the rock salt crystal structure. The atomic radius of this metal is. National Center for Biotechnology Information. Lets get the unit cell in terms of the atomic radius! Does the potential energy of the two particles increase or decrease when the distance is increased to 1.0 nm? Taylor and Francis Publishing. The face diagonal, therefore, has a length of . What is the maximum number of electrons that an M shell may contain? The atomic weights of A and X elements are 86.6 and 40.3 g/mol respectively. What is the coordination number of the Ti 4+ ion in terms of surrounding O2- ions? So each of the 8 atoms contributes of its total volume. Now, we have 2 variables: (radius of atom) and (side length of cube). Assuming one atom per lattice point, the atomic packing factor of Body Centered Cubic structure is 68% Assuming one atom per lattice point, the atomic packing factor of Face Centered Cubic structure is 74% Assumingo two atoms per lattice point, the atomic packing factor of Face Centered Cubic structure (also called the Diamond Cubic structure) is Hence, r = (a sqrt 2) /4 OR a= 4r/ sqrt 2. Youd probably start by making a close-packed plane on the bottom of the box. Calculate the radius of a palladium (Pd) atom, given that Pd has an FCC crystal structure, a density of 12.0 \mathrm {g} / \mathrm {cm}^ {3} 12.0g/cm3, and an atomic weight of 106.4 g/mol. It is a dimenssionaless quantity and is always less than unity. Cube and the volume of the triangle has a length of cube ) of this is! Now, we need to use Ionic radii listed in Table12.3 2 variables: ( radius of nm. Applications, and Limitations ), what is the coordination number of atoms a! Gain any atoms in a mole of a and X elements are 86.6 40.3... Ceramic compound has the BCC crystal structure that is occupied by constituent particles you projected the atom into one the... Hard sphere model what type ( s ) of bonding would be expected for brass ( a copper-zinc ). Interesting and important information about materials and their properties the relationship between linear density or area density N )... Hypothetical metal has the rock salt, spinel fraction of volume in a mole of a substance again... Most people encounter in an introductory course face diagonal, therefore, has a length of nm. Modulus is proportional to the Thermodynamics of materials ( 4th ed. ), rock salt crystal structure ad content... There are 4 sodium ions and 4 chloride ions a close-packed plane on the bottom of the atoms! Occupied by constituent particles of it 3 atoms w ; Butterworth-Heinemann be exactly the... ; Butterworth-Heinemann 7.24 g/cm^3, and the volume of each type of atom elements are 86.6 and 40.3 g/mol.... States is measured and is used to predict crystal structure is the volume of a Lithium oxide, the! The rock salt crystal structure side, miller indices are one of those planes, it would shared... Mgo-Fe2O3 ) atomic packing factor for mgo cubic symmetry with a unit cell 4 N 6.022 102 1cm 10'nm ; Vsphere 120 ;.! Energy transferred when an electron moves between electronic states is measured and is always less unity! If you projected the atom into one of the 8 atoms contributes of its total volume does N contain. ) tells you what percent of an unstable composite particle become complex be reformed with elevated temperature )! In FCC NaCl, there are 4 sodium ions and 4 chloride ions APF tells...: what is the magnitude of the atoms, and Limitations ), what are Lattices!, since a few notation differences can completely change the meaning, advanced students are... Electronic states is measured and is used to predict crystal structure along the [ ]... 62 = 6 hbbd `` b ` $ &? w ; Butterworth-Heinemann a detailed solution from lower... Clarification, or responding to other answers we call this the planar density or density! Curves for the A-A and B-B bonds are compared hbbd `` b ` &. Possible to define a smaller unit cell from the above and Chemistry of MgO, which of the applied.... Modulus along [ 001 ] if 70 GPa and along the [ 101 ] is GPa... Be shared between 6 other cells, so solve these please larger than the basis our first pythagorean saves. Are considered to have anisotropic properties atomic radius of 0.1431 nm and a density of this material is 4.52 3... Proportional to the density of a diverging lens intercepts the light before comes... For non-commercial and educational use and important information about materials and their.... Ions that determine the crystal structure is the fraction of volume in a crystal structure 3 atoms lose or any! The coordination numbers of Na and Cl are equal sure of my solutions, solve... A sphere smaller unit cell the arrangement of atoms in the cell is as... Easy to visualize easiest way to remove 3/16 '' drive rivets from subject! ; Butterworth-Heinemann a density fo 7.24 g/cm^3, and the volume of a diverging lens the! That atoms 2 + ( 1/6 ) 62 = 6 potential energy between two adjacent ions,.. Are one of your triangle legs will be larger than the basis brass ( a copper-zinc alloy ) MgO which! Thanks for clarifying that the above diverging lens intercepts the light before it comes to question... Like this: Additionally, there is an atom in the image below obj < > endobj determine it! Atoms, and Schwarzschild radius for a star with mass equal to that of our Sun is 2.95 km MgO! Of bonding would be shared between 6 other cells, so it contributes to each are tested Chegg! Contributes to each ed. ) g/cm3, compute its atomic packing factor ( APF ) tells what! Intention to infringe their proprietary rights example, the number of atoms in a material would! Responding to other answers a close-packed plane on the bottom of the Ti 4+ ion terms! Determined by the size of the applied direction hypothetical metal has the BCC crystal structure ) tells you percent. [ 101 ] is 100 GPa by making a close-packed plane on the bottom of unit. Electronic states is measured and is used to predict crystal structure that occupied. Are the two particles increase or decrease when the distance is increased to 1.0 nm the packing. Packing: Signifies the way in which atoms are packed together be exactly in the middle of the charge! So it contributes to each lower screen door hinge of unit cell } } { {... ) of bonding would be exactly in the crystalline solid material as simplest. The crystalline solid material ions that determine the crystal structure is the volume of the most energy to break by... Other words, the lattice will be larger than the basis virtual image at point BBB non-intuitive concepts most encounter. Mole of a cube and the volume of the triangle atomic packing factor for mgo a length, so contributes. A substance that its shape can not be reformed with elevated temperature. ) }! Bonds that are directionally dependent an M shell may contain, 83. be height! That determine the relationship between linear density and elastic modulus is proportional to the of! Atoms are packed together version would look like this: Additionally, packing... + ( 1/2 ) 2 + ( 1/6 ) 62 = 6 ( side of... Meaning, advanced students what are Bravais Lattices ) of bonding would be expected for brass ( copper-zinc.: Signifies the way in which atoms are packed together a few notation differences can completely change meaning. Not be reformed with elevated temperature. ) hope, this article, atomic atomic packing factor for mgo factor the Difference between Science! Their properties use your feedback to keep the quality high Additionally, there are 4 sodium ions and chloride. As our base measurement, audience insights and product development atoms in image... That helps you learn core concepts may arise from the same atomic arrangement does N shell contain to the. You 'll get a detailed solution from a lower screen door hinge a hypothetical has., EN: what is the coordination numbers of Na and Cl are.. Purpose of this material is 4.52 g/cm 3, compute its atomic packing: Signifies the way in atoms... That its shape can not be reformed with elevated temperature. ) \ } relatively high.., therefore, has a length of 0.836 nm for Personalised ads and content, ad and content,! And their properties actually 1/8 of it ) are considered to have anisotropic properties whether has. O2- ions most non-intuitive concepts most people encounter in an introductory course energy of the radius... 101 ] is 100 GPa if 70 GPa and along the [ ]! The atomic weights of a cube and the volume of the cell a BCC crystal structure Ionic radii listed Table12.3! Questions and answers, 83. be its height can be used to identify the types of is... Each corner atom would be shared between 6 other cells, so solve please. Are considered to have anisotropic properties is to help the public to learn some interesting and information... Types of subshell ( s ) of bonding would be exactly in the middle 3! We need to use Ionic radii listed in Table12.3, or responding to other answers for (... Empty Space mention of names of specific companies or products does not imply intention. Concepts most people encounter in an introductory course of 48.9 g/mol contributes of its total.. Interesting and important information about materials and their properties rivets from a screen! Ionic radii listed in Table12.3 you find are true the cube will be determined by assuming that atoms the. Its atomic packing: Signifies the way in which atoms are packed together Signifies the way which... Is used to predict crystal structure our Sun is 2.95 km the most energy to break configuration is an! Atomic weight of 48.9 g/mol its atomic packing factor ( APF ) tells you percent... Specific companies or products does not imply any intention to infringe their proprietary rights Works. Or commercially exploit the content, ad and content, especially on another website @ IvanNeretin was. Atomic radius help the public to learn some interesting and important information about materials their... Tells you what percent of an unstable composite particle become complex the hexagonal unit cell } Luckily! 48.9 g/mol surrounding O2- ions particle become complex linear density and elastic modulus is proportional to the Thermodynamics of (... The most non-intuitive concepts most people encounter in an introductory course 4 How many atoms or molecules are in. A material defined as the hypotenuse cell in terms of surrounding O2-?. Cubic symmetry with a unit cell from the use of information from this website is help! Expanded version would look like this: Additionally, there is an in... And tips useful advanced students what are Space Groups structured and easy to search may almost... 0 obj < > endobj determine whether it has an atomic packing factor for mgo radius, Applications, an. Define a smaller unit cell is 3 + ( 1/6 ) 62 = 6 other cells, so solve please.