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JEE Advanced
Exam
JEE Advanced
Subject
Chemistry
Chapter
Solid State

JEE Advanced · Chemistry · Solid State

Paragraph: A solid crystal is composed of X, Y and Z atoms, Z atoms...

Paragraph: A solid crystal is composed of X,YX, Y and ZZ atoms, ZZ atoms (radius 200 pm ) form cubic close packed structure, whereas XX (radius 50 pm )andYand Y (radius 100 pm ) occupy respective voids - Assume all the voids are occupied. Now answer the following questions.Question: If all the atoms along one body diagonal are removed, then the formula of the compound becomes :

Options

  1. AX8Y4Z5\mathrm{X}_8 \mathrm{Y}_4 \mathrm{Z}_5
  2. BX8Y4Z4\mathrm{X}_8 \mathrm{Y}_4 \mathrm{Z}_4
  3. CX6Y3Z3\mathrm{X}_6 \mathrm{Y}_3 \mathrm{Z}_3
  4. DX6Y3Z4\mathrm{X}_6 \mathrm{Y}_3 \mathrm{Z}_4

Correct answer

A. X8Y4Z5\mathrm{X}_8 \mathrm{Y}_4 \mathrm{Z}_5

Step-by-step solution

In the original compound ZZ atoms → form CCP X atoms → present in tetrahedral void. (rXrZ=50200=0.25)\left(\frac{r X}{r Z}=\frac{50}{200}=0.25\right) Y atoms → present in octahedral void (rYrZ=100200=0.5)\left(\frac{r Y}{r Z}=\frac{100}{200}=0.5\right) Assuming, all voids are occupied, formula of the original compound =X8Y4Z4=X_8 Y_4 Z_4. On removing atoms along one body diagonal, We lose →2Z\rightarrow 2 Z atoms, 2X2 X atoms, 1Y1 Y atom (body centre) ∴\therefore The new formula becomes →X6Y3Z3.75\rightarrow \mathrm{X}_6 \mathrm{Y}_3 \mathrm{Z}_{3.75} Simplest formula →X8Y4Z5\rightarrow \mathrm{X}_8 \mathrm{Y}_4 \mathrm{Z}_5
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