Work Function in Metals: Determine whether the statement "Work function is the maximum energy required by the fastest electron at 0 K to escape from the metal surface" is true or false.

Introduction / Context:
The concept of work function is fundamental in solid-state physics and electronics. It governs electron emission phenomena such as thermionic emission, photoelectric effect, and field emission. Understanding its correct definition ensures clarity when analyzing device physics like cathodes, photocells, and semiconductor-metal contacts.

Given Data / Assumptions:

• Material is a pure metal at absolute zero (0 K).
• Statement: "Work function is the maximum energy required by the fastest electron at 0 K to escape from the metal surface."

Concept / Approach:

The work function (Φ) is defined as the minimum energy required to remove an electron from the Fermi level of a metal to a point just outside the surface (vacuum level). At 0 K, the highest-energy electrons occupy the Fermi level. Thus, the energy difference between the vacuum level and the Fermi level represents the work function.

Step-by-Step Solution:

Verification / Alternative check:

Photoelectric emission experiments confirm that the threshold photon energy equals the work function. At 0 K, the fastest electrons are at E_F, so the definition matches practical measurements.

Why Other Options Are Wrong:

• 'False': Contradicts the well-established definition.
• 'True only for semiconductors': Misleading; definition applies to metals and semiconductors alike.
• 'False, depends on temperature': Temperature influences electron population above E_F but does not redefine Φ.
• 'Cannot be determined': Incorrect because the definition is standard.

Common Pitfalls:

• Confusing 'minimum energy required' with 'maximum electron energy available' — at 0 K, these coincide because only electrons at the Fermi level can escape.
• Believing that work function changes at 0 K — while thermal effects exist, the base definition is independent of operating temperature.

Final Answer:

True