Quantum Mechanics

Step 1: The energy required for the electron to escape is given as: Step 2: The wavelength of the emitted electron can be found using the de Broglie equation: where , and is Planck's constant, is the mass of the electron, and is the energy.

Step 3: Substituting values:

Step 1: Use Heisenberg's Uncertainty Principle where:
- nm m, - Js.
Step 2: Compute

Step 1: Applying the de Broglie Wavelength Formula
The de Broglie wavelength is given by: where is the momentum of the electron. The kinetic energy is related to momentum by: Substituting this into the de Broglie equation:

Step 2: Substituting Given Values
Given that: We substitute these values: Rewriting:

Final Answer: The correct choice is Option (2): .