Question

Assertion: The total number of atoms present in a simple cubic unit cell is one.

Reason: Simple cubic unit cell has atoms at its corners, each of which is shared between eight adjacent unit cells.

• A. Assertion and reason both are correct statements and reason is correct explanation for assertion.
  
• B. Assertion is a correct statement but reason is a wrong statement.
  
• C. Assertion is a wrong statement but reason is correct statement.
  
• D. Assertion and reason both are correct statements but reason is not correct explanation for assertion.
  

Answer 1

The correct option is A Assertion and reason both are correct statements and reason is correct explanation for assertion.


Analysing the reason :

In a simple cubic unit cell, atoms are present only at the corners. Each atom is shared by seven other unit cells. So, the contribution of a corner atom to the unit cell in consideration is $\frac{1}{8}$.

So, the reason is correct. and it explains the assertion.

Hence, both the assertion and the reason are correct statements, and the reason is the correct explanation for the assertion.

Analysing the assertion

In a simple cubic unit cell, atoms are present only at the corners and one atom is shared by $8$ adjacent cells, so the contribution of $1$ atom in a cell is $\frac{1}{8}$. Since there are 8 corners, the total number of atoms present is = $\frac{1}{8}\times 8=1$

So, the assertion is correct.

So, option (A) is the correct answer.