Question

The product particles having radius less than critical radius ($r_c$) during nucleation are known as

• A. Nuclei
• B. Embryos
• C. Elements
• D. Atoms

Hint:

Embryos are unstable clusters; only when they exceed the critical radius do they become stable nuclei.

Answer 1

The Correct Option is B

Step 1: Understanding nucleation.
Nucleation is the initial process during a phase transformation where small clusters of atoms form in the parent phase. These clusters may grow or dissolve depending on their size.
Step 2: Concept of critical radius.
There exists a critical radius ($r_c$) during nucleation. Clusters with radius smaller than $r_c$ are unstable and tend to dissolve back into the parent phase.
Step 3: Definition of embryos.
Clusters or particles with radius less than the critical radius are called embryos. Only those clusters that grow beyond the critical radius become stable nuclei.
Step 4: Conclusion.
Hence, product particles having radius less than the critical radius are known as embryos.

Answer 2

During nucleation, the total free energy change for forming a particle of radius \( r \) has a competition between a volume term that favours growth and a surface term that opposes it, producing a maximum at the critical radius \( r_c \). Let's use that free-energy behaviour to evaluate each option.

1. Nuclei: A nucleus, by definition, has already grown past the critical radius \( r_c \). Beyond this size, further growth continuously lowers the total free energy, so nuclei are stable and continue to grow rather than dissolve.
2. Embryos: A cluster smaller than \( r_c \) sits on the rising part of the free-energy curve, where growing larger actually raises the total free energy. Such clusters are thermodynamically unstable and tend to shrink back and disappear into the parent phase rather than grow, exactly the behaviour of particles below the critical radius, which is why they are called embryos.
3. Elements: This term refers to chemical elements, the basic substances themselves, and has no defined meaning within nucleation theory regarding cluster size.
4. Atoms: Atoms are the individual building blocks that come together to form a cluster in the first place. A sub-critical cluster made of many atoms is not itself called an atom, this term describes the individual particles, not the transient cluster they form.

Since clusters below \( r_c \) sit on the unstable, energy-raising side of the nucleation curve and tend to redissolve, they are correctly termed embryos.

Therefore, the correct answer is Embryos.