How can I explain what a kilogram is using Planck's constant?

Quoting this excellent thought experiment from the article An atomic physics perspective on the new kilogram defined by Planck’s constant by Wolfgang Ketterle (thank you wcc!):

The new kilogram may be understood as the mass difference of $1.4755214 \times 10^{40}$ Cs atoms in the ground state versus the same number in the excited hyperfine state or as the mass of $1.4755214 \times 10^{40}$ photons at the Cs hyperfine frequency trapped in a microwave cavity. The numerical value $$ 1.4755214 \times 10^{40}\,\text{kg}^{-1} = \frac{c^2}{h \cdot \nu_{Cs}} = \frac{299\ 792\ 458\,\text{m}^2\text{/s}^2}{6.626\ 070\ 15\times 10^{-34}\,\text{kg m}^2\text{/s}\ \cdot 9\ 192\ 631\ 770\,\text{s}^{-1}} $$ is fixed through the definitions of $h$, $c$ and $\nu_{Cs}$ and has no uncertainty.

In a thought experiment, one could measure out 1 kg of any substance by having a mechanical balance where the substance and the ground state Cs atoms on one side are compared with the Cs atoms in the excited hyperfine state on the other side of the balance.

So this is it! I think this is probably the best way to think about what this new definition of the kilogram actually represents: It's the difference in mass of a bunch of cesium atoms in one energy state versus another.

Energy and mass are equivalent. The two equations for energy you start with are equating the energy contained within 1kg of matter and the energy of a photon having frequency f. So, a single photon with with a frequency of 1.3564e50 Hz has the energy equivalent of 1kg of mass. As you might imagine, that is an extremely energetic photon, many orders of magnitude past where we've stopped naming parts of the electromagnetic spectrum - it'd be a super-duper-ultra-high-energy gamma wave.