Energy, temperature and the ratio E/kT

Overview

Recall questions on kT and its size at room temperature, comparing bond, band-gap and escape energies with it, why the ratio has no unit, and what a small ratio implies.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What does the quantity kT represent?

   Model answer

   It is the typical thermal energy available per particle at an absolute temperature T.

2. 2

   Calculate kT at room temperature, taking that as 293 K.

   Model answer

   kT = 1.38 × 10⁻²³ × 293 = 4.0 × 10⁻²¹ J.

3. 3

   Express kT at room temperature in electronvolts.

   Model answer

   It is about 0.025 eV, roughly one fortieth of an electronvolt.

4. 4

   Why is the ratio E/kT more informative than the energy E on its own?

   Model answer

   It says how large an energy step is compared with the thermal energy available, which is what decides whether the step is often taken.

5. 5

   Does the ratio E/kT carry a unit?

   Model answer

   No, both E and kT are energies, so the ratio is a pure number.

6. 6

   An energy step of 6.4 × 10⁻²⁰ J exists at 290 K. Calculate E/kT.

   Model answer

   kT = 1.38 × 10⁻²³ × 290 = 4.0 × 10⁻²¹ J, so E/kT = 16.

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