Question:
A compound consists of three ions X, Y, and Z. The Z ions are arranged in an FCC arrangement. The X ions occupy \(\frac{1}{6}\) of the tetrahedral voids and the Y ions occupy \(\frac{1}{3}\) of the octahedral voids. Which one of the following is the CORRECT chemical formula of the compound?
A compound consists of three ions X, Y, and Z. The Z ions are arranged in an FCC arrangement. The X ions occupy \(\frac{1}{6}\) of the tetrahedral voids and the Y ions occupy \(\frac{1}{3}\) of the octahedral voids. Which one of the following is the CORRECT chemical formula of the compound?
Show Hint
In compounds with FCC structures, tetrahedral and octahedral voids are common, and the ions occupy these voids in specific ratios. Calculate the number of ions based on these ratios to get the correct formula.
Updated On: Aug 30, 2025
- XY\(_2\)Z\(_4\)
- XYZ\(_3\)
- XYZ\(_2\)
- XYZ\(_4\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
- In an FCC arrangement, there are 4 unit cells. Each unit cell has 8 octahedral voids and 12 tetrahedral voids.
- Number of Z ions = 4 (since Z occupies all FCC lattice sites).
- Number of X ions = \(\frac{1}{6}\) of the tetrahedral voids = \(\frac{1}{6} \times 12 = 2\).
- Number of Y ions = \(\frac{1}{3}\) of the octahedral voids = \(\frac{1}{3} \times 8 = \frac{8}{3}\).
- The total number of Y ions is 3. Hence, the chemical formula is XYZ\(_3\).
- Number of Z ions = 4 (since Z occupies all FCC lattice sites).
- Number of X ions = \(\frac{1}{6}\) of the tetrahedral voids = \(\frac{1}{6} \times 12 = 2\).
- Number of Y ions = \(\frac{1}{3}\) of the octahedral voids = \(\frac{1}{3} \times 8 = \frac{8}{3}\).
- The total number of Y ions is 3. Hence, the chemical formula is XYZ\(_3\).
Was this answer helpful?
0
0
Top GATE PH Physics Questions
- An infinite one-dimensional lattice extends along the x-axis. At each lattice site, there exists an ion with spin 1/2. The spin can point either in the +z or -z direction only. Let \( S_P \), \( S_F \), and \( S_A \) denote the entropies of paramagnetic, ferromagnetic, and antiferromagnetic configurations, respectively. Which of the following relations is/are true?
- Two point charges of charge \( +q \) each are placed a distance \( 2d \) apart. A grounded solid conducting sphere of radius \( a \) is placed midway between them. Assume \( a^2 \ll d^2 \). Which of the following statements is/are true?
- A particle of mass $m$ is moving in the potential
\[ V(x) = \begin{cases} V_0 + \frac{1}{2} m \omega_{0P}^2 x^2 & \quad \text{if } x > 0 \\ \infty & \quad \text{if } x \leq 0 \end{cases} \]
Figures P, Q, R, and S show different combinations of the values of $ \omega_0 $ and $ V_0 $. - Decays of mesons and baryons can be categorized as weak, strong and electromagnetic decays depending upon the interactions involved in the processes. Which of the following option is/are true?
- The temperature \( T \) dependence of magnetic susceptibility \( \chi \) (Column I) of certain magnetic materials (Column II) are given below. Which of the following options is/are correct?
Column I Column II (1) 
(P) Diamagnetic (2) 
(Q) Paramagnetic (3) 
(R) Ferromagnetic (4) 
(S) Antiferromagnetic
View More Questions
Top GATE PH Solid State Questions
- Consider a two-dimensional Cartesian coordinate system in which a rank 2 contravariant tensor is represented by the matrix \[ \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \] The coordinate system is rotated anticlockwise by an acute angle $\theta$ with the origin fixed. Which one of the following matrices represents the tensor in the new coordinate system?
For nonrelativistic electrons in a solid, different energy dispersion relations with effective masses \(m_a^*, m_b^*, m_c^*\) are schematically shown in the plots. Which one of the following options is CORRECT?
Graphene is a two-dimensional material, in which carbon atoms are arranged in a honeycomb lattice with lattice constant $a$. As shown in the figure, $\vec{a_1}$ and $\vec{a_2}$ are two lattice vectors. Which one of the following is the area of the first Brillouin zone for this lattice?
- A symmetric top has principal moments of inertia $I_1 = I_2 = \dfrac{2\alpha}{3}$, $I_3 = 2\alpha$ about a set of principal axes 1, 2, 3 respectively, passing through its center of mass, where $\alpha$ is a positive constant. There is no force acting on the body and the angular speed of the body about the 3-axis is $\omega_3 = \dfrac{1}{8}$ rad/s. With what angular frequency in rad/s does the angular velocity vector $\vec{\omega}$ precess about the 3-axis?
- For a covalently bonded solid consisting of ions of mass \(m\), the binding potential can be assumed to be given by \[ U(r) = -\varepsilon \left( \frac{r}{r_0} \right) e^{-\frac{r}{r_0}}, \] where \(\varepsilon\) and \(r_0\) are positive constants. What is the Einstein frequency of the solid in Hz?
Top GATE PH Questions
- If \( F_1(Q, q) = Qq \) is the generating function of a canonical transformation from \((p, q)\) to \((P, Q)\), then which one of the following relations is correct?
- When an unpolarized plane electromagnetic wave in a dielectric medium with refractive index \( n_1 \) is incident on a plane interface separating it from another dielectric medium with refractive index \( n_2 \) (where \( n_2 > n_1 \)), and the angle of incidence is \(\tan^{-1} \left( \frac{n_2}{n_1} \right) \), the following statement is true:
- The wavefunction of a particle in an infinite one-dimensional potential well at time \( t \) is
\[ \Psi(x, t) = \sqrt{\frac{2}{3}} e^{-iE_1 t/\hbar}\psi_1(x) + \frac{1}{\sqrt{6}} e^{i\pi/6} e^{-iE_2 t/\hbar} \psi_2(x) + \frac{1}{\sqrt{6}} e^{i\pi/4} e^{-iE_3 t/\hbar} \psi_3(x) \]where \(\psi_1\), \(\psi_2\), and \(\psi_3\) are the normalized ground state, the normalized first excited state, and the normalized second excited state, respectively. \(E_1\), \(E_2\), and \(E_3\) are the eigen-energies corresponding to \(\psi_1\), \(\psi_2\), and \(\psi_3\), respectively. The expectation value of energy of the particle in state \(\Psi(x,t)\) is - If a thermodynamical system is adiabatically isolated and experiences a change in volume under an externally applied constant pressure, then the thermodynamical potential minimized at equilibrium is the
- The mean distance between the two atoms of an HD molecule is \( r \), where H and D denote hydrogen and deuterium, respectively. The mass of the hydrogen atom is \( m_H \). The energy difference between the two lowest lying rotational states of HD in multiples of \(\frac{h^2}{m_H r^2}\) is:
View More Questions