Question

Ques.The density of copper metal is 8.95 g cm3. If the radius of copper atom is 127.8 pm, is the copper unit cell a simple cubic, a body-centred cubic or a face centred cubic structure? (Given: At. Mass of Cu = 63.54 g mol1and NA= 6.02 × 1023mol1)
can you please explain how it is fcc?d=M.z a3.NAOn substituting we get,8.95=z.63.54 6.022X1023X(1.27X10-8)3z=0.17.please help me out! where did i go wrong?

Answer 1

Hey !!

Let me start solving this question !!

Suppose copper has fcc structure

            z = 4 , a = 2√2r

                  d = z × M/a³ × NA -----> (Equation (1))

Here, M = 63.54 g mol⁻¹ , NA = 6.022 × 10²³ mol⁻¹

a = 2√2 r = 2√2 × 127.8 pm = 2√2 × 127.8 × 10⁻¹⁰ cm

a = 3.614 × 10⁻⁸ cm

Now, Substituting these values in the expression (1), we get

             d = 4 × 63.54 g mol⁻¹/(3.614 × 10⁻⁸ cm)³ × 6.022 × 10²³ mol⁻¹

FINAL RESULT = 8.94 g cm⁻³

As the calculated value of density (8.94 g cm⁻³) is in agreement with the given value (8.95 g mol⁻¹)

Therefore, copper unit cell has face-centered cubic structure.

HOPE IT HELPS YOU !!

You have gone wrong in calculation part. Have a look on my answer and kindly repeat this question again.

GOOD LUCK !!