Home
Class 12
CHEMISTRY
An element occurs in bcc structure. It h...

An element occurs in bcc structure. It has a cell edge length of 250 pm. Calculate the molar mass if its density is 8.0 g `cm^(-3)` . Also calculate the radius of an atom of this element.

Text Solution

Verified by Experts

Given, cell edge length, `a = 250 p m = 250xx10^(-10)cm`
Density = `8g cm^(-3)`
For boc cell, number of atoms, Z = 2
Molar mass, M=?
We know that, density, `d= (Z*M)/(a^(3)*N_(A))`
or `8 g cm^(-3)= (2xxM)/((250xx10^(-10) cm)^(3) (6.022 xx 10^(23)"mol"^(-1)))`
or `M=((250xx10^(-10)cm)^(3)(6.022 xx 10^(23)"mol"^(-1)))/(2)xx 8 g cm^(-3)`
`=(9.409xx 8)/(2)`
`=37.64"g mol"^(-1)`
For bcc unit cell, `4r=sqrt(3)a`
Radius, `r=(sqrt(3)*a)/(4)=(1.732xx250)/(4)`
`=108.25` pm
Promotional Banner

Topper's Solved these Questions

  • THE SOLID STATE

    ARIHANT PUBLICATION|Exercise PART II (QUESTION FOR PRACTICE) (Long Answer Type Questions)|2 Videos

  • THE SOLID STATE

    ARIHANT PUBLICATION|Exercise PART II (QUESTION FOR ASSESSMENT) (Multiple Choice Type Questions)|3 Videos

  • THE SOLID STATE

    ARIHANT PUBLICATION|Exercise PART II (QUESTION FOR PRACTICE) (Short Answer Type I Questions)|14 Videos

  • SURFACE CHEMISTRY

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE ( LONG ANSWER TYPE QUESTIONS)|1 Videos

Similar Questions

Explore conceptually related problems

An element occurs in b c c structure with cell edge of 288 p m .Its density is 7.2 g cm^-3 . calculate the atomic mass of the element.

An element occurs in bcc structure with cell edge 300 pm. The density of the element is 5.2 g cm^(-3) . How many atoms of the element does 200 g of the element contain?

An element has a body centred cubic (bcc) structure with a cell edge of 288 pm. The density of the element is 7.2 g//cm^(3) . How many atoms are present in 208 g of the element?

A face centred cubic crystal has an edge length of 4A^@ , If atomic mass of the element is 60, find its density.

An element X with an atomic mass of 60 "g mol"^(-1) has density of 6.23 "g cm"^(-3) . If the edge length of its cubic unit cell is 400 pm, identify the cubic unit cell. Calculate the radius of an atom of this element.

An element crystallises in a bcc lattice with cell edge of 500 pm. The density of the element is 7.5 gm^(-3) . How many atoms are present in 300 g of the element ?

The edge length of unit cell of a body centred metal crystal is 352 pm. Calculate the radius of an atom of the metal.

Silver crystallises in fcc lattice. If edge length of the cell is 4.07xx10^(-8) and density is 10.5 g cm^(-3) . Calculate the atomic mass of silver.