Order of magnitude of Debye temperature for metals What is a typical order-of-magnitude value of the Debye temperature θD for common metals?

Introduction / Context:The Debye temperature θD characterizes the phonon spectrum cutoff and is a key parameter in low-temperature heat capacity, thermal conductivity, and elastic properties. Knowing its typical scale helps in estimating C_v behavior (T^3 law) and distinguishing material classes.

Given Data / Assumptions:

• “Typical” metals at room temperature and below.
• θD values vary widely across elements (tens to several hundreds of kelvin).
• Order-of-magnitude choice rather than an exact number.

Concept / Approach:

For many common metals, θD lies on the order of 10^2 K. Examples: Pb ~ 105 K, Au ~ 170 K, Cu ~ 343 K, Al ~ 428 K, Fe ~ 470 K. Some light or stiff materials can have even higher values, while heavy, soft metals have lower θD. Thus, “about 200 K” best represents a central order-of-magnitude for metals as a class.

Step-by-Step Solution:

Verification / Alternative check:

Solid-state tables list θD for many metals in the 100–500 K range; this confirms the 10^2 K scaling.

Why Other Options Are Wrong:

10 K or 2 K are too low for metals in general; 600 K can occur (e.g., Be) but is not “typical” for the broad class; 10,000 K is nonphysical for θD.

Common Pitfalls:

Assuming a single θD fits all metals exactly; θD is element-specific and influenced by bonding stiffness and atomic mass.

Final Answer:

About 200 K