An element with molar mass 2.7 × 10?2 kg mol?1 forms a cubic unit cell with edge length 405 pm Chapter 1: the Solid State Chemistry Class 12 solutions are developed for assisting understudies with working on their score and increase knowledge of the subjects. Question 1.18: An element with molar mass 2.7 × 10−2 kg mol−1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 × 103 kg m−3, what is the nature of the cubic unit cell? is solved by our expert teachers. You can get ncert solutions and notes for class 12 chapter 1 absolutely free. NCERT Solutions for class 12 Chemistry Chapter 1: the Solid State is very essencial for getting good marks in CBSE Board examinations

Question 1.18: An element with molar mass 2.7 × 10⁻² kg mol⁻¹ forms a cubic unit cell with edge length 405 pm. If its density is 2.7 × 10³ kg m⁻³, what is the nature of the cubic unit cell?

Answer
Given that
             Density of element, p = 2.7 × 10³ kg m⁻³
             Molar mass, M           = 2.7 × 10⁻² kg mol⁻¹
             Edge length, a           = 405 pm
1 pm = 10⁻¹² meter
So edge in meter              = 405 × 10⁻¹² m = 4.05 × 10⁻¹⁰ m
Let Z is the number of atoms in unit cell
Number of atoms in 1 mol of substance, NA = 6.022 × 10²³ atoms
Use formula
Density

$p=/frac{ZM}{{{a}^{3}}{{N}_{A}}}$

Cross multiply we get
< pa³N_A= ZM
Divide by M we get

/[Z=/frac{p{{a}^{3}}{{N}_{A}}}{M}/]

Now plug the values we get

$/Rightarrow Z=/frac{2.7x{{10}^{3}}(4.05x{{10}^{-10}})(6.022x{{10}^{23}})}{2.7x{{10}^{-2}}}$

Hence there are four atoms of the element are present per unit cell So that, this unit cell can a face−centred cubic (fcc) or cubic close−packed (ccp).

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An Element With Molar Mass 2.7 × 10?2 Kg Mol?1 Forms a Cubic Unit Intext Questions Chapter 1 the Solid State

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