Consider a particle of mass m in a cubic container of volume V. Show that the separation of successive energy levels is given approximately by ΔE≈π2ℏ2/2mV2/3, and roughly evaluate ΔE for helium atoms in a container of volume one m3. Show that, for any temperature higher than ≈10−8 K, the quantum mechanical partition sum can be approximated well by an integral. Show that this ``approximation'' leads to equation 16.70.