A hypothetical system consists of four molecules with a total energy 4$\varepsilon$Calculate the total number of ways of distributing four quanta of energy $\varepsilon$ amongst the four molecules.

Question

Quizplus · Accepted Answer

The problem is a combinatorial one where we need to distribute 4 indistinguishable quanta of energy among 4 distinguishable molecules. This is a classic "stars and bars" problem, where the number of ways to distribute n indistinguishable items into k distinguishable bins is given by the formula (n+k-1) choose (k-1). Here, n=4 and k=4, so the number of ways is (4+4-1) choose (4-1) = 7 choose 3 = 35.

A Hypothetical System Consists of Four Molecules with a Total ε\varepsilonε

A Hypothetical System Consists of Four Molecules with a Total $\varepsilon$