An element has a bcc structure with a celledge of `288` pm. The density of the element is `7.2 g cm^(-3)`. How many atins are present in `208 g` of the element?

Options

A. `24.16times10^(25)`
B. `24.16times 10^(23)`
C. `24.16times10^(24)`
D. `24.16times10^(26)`

Answer

B

Explanation

Volume of the unit cell `=(288"pm")^(3)`
`=(288times10^(-12)m)^(3)`
`=23.9times10^(-24)cm^(3)`
Volume of 208 g of the element `=(208g)/(7.2g cm^(-3))=28.88 cm^(3)`
Number of unit cells in this volume `=(28.88)/(23.9times10^(24)) `
=`12.08times10^(23)" unit cell "`
`" Each b.c.c. cube contains 2 atoms "`
`therefore" Total number of atoms in 208 g is" `
`=2times12.08times10^(23)`
`=24.16times10^(23)" atom"`.