The radius of the largest sphere which fits properly at the centre of the edge of body centred cubic unit cell is : (Edge length is represented by 'a') :
- 0.134 a
- 0.027 a
- 0.067 a
- 0.047 a
The Correct Option is C
Solution and Explanation
$a = 2\left(R + r\right) $
$\frac{a}{2} =\left(R+r\right)$ .....(1)
$ a\sqrt{3} =4R $ .....(2)
Using (1) & (2)
$ \frac{a}{2} = \frac{a\sqrt{3}}{4} =r$
$ a\left(\frac{2-\sqrt{3}}{4}\right)=r $
$ r=0.067\, a $
Top Questions on The solid state
- A metal crystallizes in simple cubic lattice. The volume of one unit cell is \( 6.4 \times 10^{-7} \, \text{pm}^3 \). What is the radius of the metal atom in pm?
- AP EAPCET - 2025
- Chemistry
- The solid state
- A metal crystallises in two cubic phases, fcc and bcc with edge lengths 3.5 Å and 3 Å respectively. The ratio of densities of fcc and bcc is approximately
- TS EAMCET - 2025
- Chemistry
- The solid state
- How many kinds of Bravais lattice are possible in a crystal?
- Bihar Board XII - 2025
- Chemistry
- The solid state
- The percentage of free space in a body-centred cubic unit cell is
- Bihar Board XII - 2025
- Chemistry
- The solid state
- The number of atoms present in body-centred cubic unit cell is
- Bihar Board XII - 2025
- Chemistry
- The solid state
Questions Asked in JEE Main exam
- The formation enthalpies, \( \Delta H_f^\circ \) for \( \text{H}_2 \) and \( \text{O}_2 \) are 220.0 and 250.0 kJ mol\(^{-1}\), respectively, at 298.15 K, and \( \Delta H_f^\circ \) for \( \text{H}_2\text{O} \) (g) is -242.0 kJ mol\(^{-1}\) at the same temperature. The average bond enthalpy of the O-H bond in water at 298.15 K is:
- JEE Main - 2025
- Thermodynamics
- In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is:
- JEE Main - 2025
- Permutations
For the AC circuit shown in the figure, $ R = 100 \, \text{k}\Omega $ and $ C = 100 \, \text{pF} $, and the phase difference between $ V_{\text{in}} $ and $ (V_B - V_A) $ is 90°. The input signal frequency is $ 10^x $ rad/sec, where $ x $ is:
- JEE Main - 2025
- AC Circuits
Two parabolas have the same focus $(4, 3)$ and their directrices are the $x$-axis and the $y$-axis, respectively. If these parabolas intersect at the points $A$ and $B$, then $(AB)^2$ is equal to:
- JEE Main - 2025
- Parabola
A point particle of charge \( Q \) is located at \( P \) along the axis of an electric dipole 1 at a distance \( r \) as shown in the figure. The point \( P \) is also on the equatorial plane of a second electric dipole 2 at a distance \( r \). The dipoles are made of opposite charge \( q \) separated by a distance \( 2a \). For the charge particle at \( P \) not to experience any net force, which of the following correctly describes the situation?
- JEE Main - 2025
- Electrostatics and Work Done by Electric Field
Concepts Used:
Solid State
Solids are substances that are featured by a definite shape, volume, and high density. In the solid-state, the composed particles are arranged in several manners. Solid-state, in simple terms, means "no moving parts." Thus solid-state electronic devices are the ones inclusive of solid components that don’t change their position. Solid is a state of matter where the composed particles are arranged close to each other. The composed particles can be either atoms, molecules, or ions.
Types of Solids:
Based on the nature of the order that is present in the arrangement of their constituent particles solids can be divided into two types;
- Amorphous solids behave the same as super cool liquids due to the arrangement of constituent particles in short-range order. They are isotropic and have a broad melting point (range is about greater than 5°C).
- Crystalline solids have a fixed shape and the constituent particles are arranged in a long-range order.