A metallurgical research laboratory analyzed three different metallic alloys (P, Q, and R)… — JAMB UTME

A metallurgical research laboratory analyzed three different metallic alloys ( $P$ , $Q$ , and $R$ ) to evaluate their internal lattice structures and physical property modifications relative to their primary base metals:

- Sample $P$ : Consists of copper with $30\%$ zinc solute atoms.
- Sample $Q$ : Consists of iron with $1.0\%$ carbon solute atoms.
- Sample $R$ : Consists of aluminium alloyed with small amounts of copper, magnesium, and manganese.

Which of the following statements correctly classifies the lattice alloy types of $P$ , $Q$ , and $R$ and accurately describes their electrical conductivity relative to their pure base metals?

Sample $P$ and Sample $R$ are substitutional alloys, while Sample $Q$ is an interstitial alloy; all three alloys exhibit lower electrical conductivity than their pure base metals due to lattice distortion.Answer
B
Sample $P$ and Sample $Q$ are interstitial alloys, while Sample $R$ is a substitutional alloy; all three alloys exhibit higher electrical conductivity than their pure base metals due to enhanced metallic bonding.
C
Sample $Q$ is a substitutional alloy, while Sample $P$ and Sample $R$ are interstitial alloys; Sample $Q$ exhibits lower electrical conductivity, whereas Sample $P$ and Sample $R$ exhibit unchanged conductivity.
D
Sample $P$ , Sample $Q$ , and Sample $R$ are all interstitial alloys; their electrical conductivity remains higher than that of pure copper, iron, and aluminium respectively because solute atoms donate free electrons to the delocalized sea.

Answer

Sample P and Sample R are substitutional alloys, while Sample Q is an interstitial alloy; all three alloys exhibit lower electrical conductivity than their pure base metals due to lattice distortion.

The correct option accurately identifies that brass (Sample P) and duralumin (Sample R) are substitutional alloys because their solute atoms have comparable atomic radii to their host atoms, whereas carbon steel (Sample Q) is an interstitial alloy because carbon atoms are small enough to enter the voids of the iron lattice. Furthermore, it correctly states that all alloys suffer a reduction in electrical conductivity relative to pure host metals due to electron scattering caused by lattice distortion.

Step-by-Step Solution

Determine the alloy lattice type for Sample P (brass) and Sample R (duralumin).

Zinc atoms (in brass) and copper/magnesium/manganese atoms (in duralumin) have atomic radii within

15\%

of the host copper and aluminium radii, so they replace host atoms directly in the crystal lattice, forming substitutional alloys.

When solute and solvent atomic radii are comparable, solute atoms substitute for host metal atoms at lattice sites.

Determine the alloy lattice type for Sample Q (carbon steel).

Carbon has a significantly smaller atomic radius than iron, allowing carbon atoms to fit into the interstitial voids between iron atoms, forming an interstitial alloy.

Solute atoms with radii much smaller than the host metal fit into spaces (interstices) between lattice atoms.

Evaluate the effect of alloying on electrical conductivity.

The presence of foreign solute atoms (whether substitutional or interstitial) causes lattice distortion, which disrupts the uniform periodic potential of the metal lattice and scatters conduction electrons, resulting in lower electrical conductivity compared to pure base metals.

Electron mobility is reduced by lattice irregularities and strain fields created by solute atoms.

Key Concept

Classification of substitutional vs interstitial alloys and the effect of lattice distortion on physical properties like electrical conductivity.

Estimated Time:2m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic