Final Answer:
The Gurney-Mott Theory describes electron emission phenomena, particularly in the context of field emission. It involves concepts such as barrier tunneling, quantum mechanics, field enhancement factor, and current density. The correct option is 1.
Step-by-step explanation:
The Gurney-Mott Theory is fundamental in understanding electron emission, particularly in the phenomenon of field emission. Field emission refers to the process where electrons tunnel through a potential barrier when subjected to a strong electric field. The Gurney-Mott Theory is crucial in explaining this phenomenon by incorporating quantum mechanics into the analysis. According to the theory, electrons overcome a potential barrier through tunneling, a quantum mechanical process where particles penetrate a classically forbidden region. Mathematically, this is expressed by the Schrödinger equation, where the probability of tunneling is influenced by the barrier height and width.
Barrier tunneling, as described by the Gurney-Mott Theory, plays a pivotal role in determining the field enhancement factor. The field enhancement factor represents the amplification of the applied electric field near a sharp emitter, enhancing electron emission. It is calculated as the ratio of the electric field at the emitter's surface to the applied field. Understanding barrier tunneling allows for the estimation and optimization of the field enhancement factor, influencing the efficiency of electron emission sources.
Moreover, the Gurney-Mott Theory is also relevant to current density in field emission. Current density is the amount of current flowing per unit area. The theory helps explain how the applied electric field, emitter properties, and quantum mechanical effects collectively influence the current density in field emission. By considering these factors, the Gurney-Mott Theory contributes significantly to the understanding and engineering of electron emission devices. Therefore the option 1. is correct.