Question

A compound is formed by two elements A and B. The element B forms cubic close packed structure and atoms of A occupy $\frac 13$ of tetrahedral voids. If the formula of the compound is A,By. then the value of x +y is in option

• A. 4
• B. 3
• C. 2
• D. 5

Answer 1

Answer: (D)

5

Answer 2

Number of tetrahedral voids = 2 x Number of atoms of B
Number of atoms of A = $\frac 13$ x Number of tetrahedral voids
Let the number of atoms of B be "x" and the number of atoms of A be "y."
From the given information, we have the equations:
x = Number of atoms of B
y = $\frac 13$ * 2x = $\frac {2x}{3}$
Since the formula of the compound is AB, the total number of atoms in the compound is x + y.
Total number of atoms = x + y = x + $\frac {2x}{3}$ = $\frac {2x}{3}$
So, the value of x + y is $\frac {5x}{3}$.
Since we are looking for the value of x + y in terms of a constant value, we can simplify the fraction by choosing a suitable value for x. Let's choose x = 3 (which is a common choice in these types of problems):
x = 3y = $\frac {2x}{3}$ = 2
So, x + y = 3 + 2 = 5.

Therefore, the correct option is (D): 5