Planck's constant does have units of energy per oscillation. Or to be exact, it has units of energy per frequency of oscillation, e.g. Joules per Hertz (J / s^

Planck's constant does have units of energy per oscillation. Or to be exact, it has units of energy per frequency of oscillation, e.g. Joules per Hertz (J / s^-1) = J s.