Question

The unit 1 electronvolt (1 eV) is defined as the energy acquired by an electron as it moves through a potential difference of 1 V. Suppose two states differ in energy by 1.0 eV. What is the ratio of their populations at (a) 300 K and (b) 3000 K?

Answer 1

Answer:

a) $1.6x10^{-17}$

b) 0.021

Explanation:

The ratio of populations (r) is given by the equation:

$r = e^{-\frac{DE}{kT} }$

Where DE is the difference between the states, k is the Boltzmann constant (k = $1.38x10^{-23} m^2.kg/s^2$, and T is the temperature in Kelvin.

So, DE = 1 eV = $1.6x10^{-19}$ J

a) For T = 300 K

r = $e^{-1.6x10^{-19}/1.38x10^{-23}x300}$

r = $1.6x10^{-17}$

b) For T = 3000 K

r = $e^{-1.6x10^{-19}/1.38x10^{-23}x3000}$

r = 0.021