That is not entirely true , the atoms themselves do not become less dense . The atoms retain mass but the molecules become spread out more sparesly making the volume less dense . However , yes the volume becomes less dense <m/V but the total energy of the volume increases >u=hf/V . The increase in energy state is the real quantum explanation as I have provided and the reason why the balloon rises , Buoyancy is not correct .
That is entirely true. Hot air rises because it is less dense then colder air.
BTW, what is your PHD in?