Copper crystallises in fcc unit cell with cell edge length of 3.608 x 10-8 cm. The density of copper is 8.92 g cm-3. Calculate the atomic mass of copper
Copper crystallises in fcc unit cell with cell edge length of 3.608 x 10-8 cm. The density of copper is 8.92 g cm-3. Calculate the atomic mass of copper
- 63.1 u
- 31.55 u
- 60 u
- 65 u
The Correct Option is A
Solution and Explanation
To find the atomic mass of copper, we use the formula for density:
Density (d) = Mass of atoms in the unit cell / Volume of the unit cell
We are given:
- Density, d = 8.92 g cm-3
- Edge length of unit cell, a = 3.608 x 10-8 cm
For a face-centered cubic (fcc) unit cell, there are 4 atoms per unit cell. The volume of the unit cell, V, is:
V = a3 = (3.608 x 10-8)3 cm3
Then, calculate:
V = 3.6083 x 10-24 = 4.695 x 10-23 cm3
The mass of the unit cell is the product of the number of atoms per unit cell, the atomic mass (M), and the conversion factor to grams (divided by Avogadro's number, NA):
Mass = (4 x M) / NA
Avogadro's number, NA = 6.022 x 1023 mol-1. Substitute the known values in the density equation:
8.92 = [(4 x M) / (6.022 x 1023)] / (4.695 x 10-23)
Solving for M:
8.92 = (4M / 6.022) / 4.695
8.92 x 4.695 = 4M / 6.022
41.86644 = 0.664M
M = 41.86644 / 0.664
M = 63.059 g/mol
Thus, the atomic mass of copper is approximately 63.1 u.
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 solution is prepared by adding 124 g of ethylene glycol (molar mass = 62 g mol\(^{-1}\)) to \( x \) g of water to get a 10 m solution. What is the value of \( x \) (in g)?
- AP EAPCET - 2025
- Chemistry
- The solid state
- The composition of a sample of wustite is \( \text{Fe}_{0.93} \text{O}_{1.00} \). Percentage of iron in the form of \( \text{Fe}^{3+} \) ion is nearly:
- AP EAPCET - 2025
- Chemistry
- The solid state
- An element (atomic weight = 250 u) crystallises in a simple cubic lattice. If the density of the unit cell is \( 7.2 \, \text{g cm}^{-3} \), what is the radius (in \( \text{\AA} \)) of the atom of the element? (\(N = 6.02 \times 10^{23} \, \text{mol}^{-1}\))
- AP EAPCET - 2025
- Chemistry
- The solid state
- The composition of a sample of wustite is \( \text{Fe}_{0.93} \text{O}_{1.00} \). Percentage of iron in the form of \( \text{Fe}^{3+} \) ion is nearly:
- AP EAPCET - 2025
- Chemistry
- The solid state
Questions Asked in NEET exam
- A photon and an electron (mass \(m\)) have the same energy \(E\). The ratio \( \frac{\lambda_{\text{photon}}}{\lambda_{\text{electron}}} \) of their de Broglie wavelengths is: (\(c\) is the speed of light)
- NEET (UG) - 2025
- Dual nature of radiation and matter
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :
- NEET (UG) - 2025
- Pendulums
- De-Broglie wavelength of an electron orbiting in the \(n = 2\) state of hydrogen atom is close to (Given Bohr radius = 0.052 nm):
- NEET (UG) - 2025
- de broglie hypothesis
- The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant \(K_1\) and \(K_2\) with thickness \(d/2\) and \(d/2\) respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If \(K_1 = 1.25 K_2\), the value of \(K_2\) is :
- NEET (UG) - 2025
- Capacitors and Capacitance
- A wire of resistance \(R\) is cut into 8 equal pieces. From these pieces, two equivalent resistances are made by adding four of these together in parallel. Then these two are added in series. The net effective resistance of the combination is:
- NEET (UG) - 2025
- Resistance
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.