An atomic substance A of molar mass 12 g mol^-1 has a cubic crystal structure with edge length of 300 pm. The no. of atoms present in one unit cell of A is (Nearest integer) Given the density of A is…

Question

An atomic substance A of molar mass 12 g mol^-1 has a cubic crystal structure with edge length of 300 pm. The no. of atoms present in one unit cell of A is (Nearest integer) Given the density of A is 3.0 g mL^-1 and N_A=6.02 10^23 mol^-1

Accepted Answer

Correct answer: 4. (4) Given: Atomic substance A with molar mass M=12 g mol^-1 Cubic crystal structure with edge length a=300 pm=300 10^-12 m Density =3.0 g mL^-1 Avogadro's number N_A=6.02 10^23 mol^-1 First, calculate the volume of the unit cell V=a^3=(300 10^-12 m)^3=27 10^-30 m Next, calculate the mass of the unit cell using the given density. Density is mass over volume, so mass m= V=3.0 g mL^-1 27 10^-30 m^3 1 mL10^-6 m^3=81 10^-24 g Then, calculate the number of moles in one unit cell The molar mass is mass over number of moles, so n= mM= 81 10^-24 g12 g mol^-1=6.75 10^-26 mol. Finally, calculate the number of atoms in one unit cell. The Avogadro constant is the number of atoms per mole, so number of atoms =n N_A=6.75 10^-26 mol 6.02 10^23 mol^-1=4.06 Rounding to the nearest integer, we get 4 atoms. So, there are 4 atoms present in one

$An atomic substance A of molar mass 12 g mol^{- 1} has a cubic crystal structure with edge length of 300 pm. The no. of atoms present in one unit cell of A is (Nearest integer) Given the density of A is 3.0 g mL^{- 1} and N_{A} = 6.02 \times 10^{23} mol^{- 1}$

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