Question

To emit an electron from the metal, the minimum electric field required is ….. 

Hint:

For field emission, an extremely high electric field (\( \sim 10^8 \) Vm\(^{-1}\)) is required to pull electrons out of a metal surface by overcoming the work function.

Answer 1

Step 1: Understanding Electron Emission 
Electron emission from a metal surface requires an external influence to overcome the work function (\( \phi \)), which is the minimum energy required to remove an electron. 
Step 2: Role of Electric Field in Electron Emission 
- The electric field (\( E \)) required for field emission of electrons is determined by: \[ E = \frac{\phi}{e d} \] where:
- \( \phi \) is the work function of the metal (in joules),
- \( e \) is the charge of an electron (\( 1.6 \times 10^{-19} \) C),
- \( d \) is the separation distance over which the field is applied. - For most metals, experimental values show that a minimum electric field of approximately: \[ 10^8 \, {Vm}^{-1} \] is required to achieve electron emission. 
Step 3: Conclusion 
The minimum electric field required to emit an electron from a metal is approximately \( 10^8 \) Vm\(^{-1}\).