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For two isomorphous crystals A and B , t...

For two isomorphous crystals A and B , the ratio of density of A to that of B is 1.6 while the ratio of the edge length of B to that of A is 2. If the molar mass of crystal B is 200 g `mol^(-1)`, then that of crystal A is

A

`"240 g mol"^(-1)`

B

`"120 g mol"^(-1)`

C

`"80 g mol"^(-1)`

D

`"40 g mol"^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Density of the unit cell , `rho=(ZxxM)/(a^3xxN_A)`
Given: `rho_A/rho_B=1.6, a_B/a_A=2, M_B` =200 g/mol
`rho_A=(ZxxM_A)/((a_A)^3xxN_0),rho_B=(ZxxM_B)/((a_B)^3xxN_0)`
(Z will be same for isomorphous crystals.)
`rho_A/rho_B=M_A/M_Bxx(a_B/a_A)^3 rArr 1.6=M_A/200xx(2)^3`
`M_A=(1.6xx200)/8`=40 g/mol
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