If `V_0` is the volume of a standard unit cell of germanium crystal containing `N_0` atoms, then the expression for the mass m of a volume V in terms of `V_0, N_0, M_("mol")` and `N_A` is [here, M is the molar mass of germanium and `N_A` is the Avogadro's constant]

Options

A. `M (V)/(V_0) (N_A)/(N_0)`
B. `(N_A)/(N_0)(V_0)/(V) M`
C. `M (V)/(V_0) (N_0)/(N_A)`
D. `M(V_0)/(V) (N_0)/(N_A)`

Answer

C

Explanation

Number of unit cells in volume V
` = ("Total volume")/("Volume of a unit cell ") = (V)/(V_0)`
Number of atoms in volume V
= Number of unit cells x Number of atoms in 1 unit cell ` = (V)/(V_0) xx N_0`
Number of moles in volume V
` = "(Number of atoms")/("Avagardo number") = (V)/(V_0) xx (N_0)/(N_A)`
Mass n of given sample volume
= Number of moles x Molar mass
` rArr m = (V)/(V_0) xx (N_0)/(N_A) xx M`