See Griffiths' QM (2nd edition), problem 1.18. Generally, quantum effects become important at temperatures
wehre is a characteristic size of the system (interatomic spacing, for instance). Try to estimate this temperature for reasonable and and you will see that the temperature will be less than one Kelvin for most situations.
When is very small (in particular, less than 1 K), than, obviously, exceeds . Of course, proportionality factors are also important, but if the temperature is extremely small (and it is, for most situations) than and, therefore,