Question

Introduction to Thermodynamics and Statistical Mechanics Problem 12.11 Carter

Calculate the value of n_j in which an oxygen atom confined to a cubical box 1cm on each side will have the same energy as the lowest energy available to a helium atom confined to a cubical box 2 x 10⁻¹⁰m on each side. Please explain your reasoning and your work.

Answer 1

energy of a particle in a cubical box is given by

, where

for helium atom, lowest energy is available for

, also mass of Helium,

volume

so

for oxygen , ,   

according to question,