Richard Rhodes: X-Ray Flux has Mass?

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On pp. 459 of Dark Sun: The Making of the Hydrogen Bomb Richard Rhodes writes:
...atomic bomb produces an enormous flux of radiant energy; if a cube of that massless flux could somehow be cut out and weighed it would reveal itself to be nearly as heavy as an equivalent cube of air.

He is talking about soft-x-rays in that quote. I understand that X-rays are massless so their weight is zero regardless of the density of the flux. Is this not correct? Is there a better comparison he could have used to describe the density of the X-ray flux?
 
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Photons as particles do not have mass, but if you consider the total energy of a box at rest (with radiation inside), it has a mass equivalent to its energy content (divided by c^2).
In the same way, a proton has a mass of ~940 MeV/c^2, while its (valence) quarks inside just have mass of ~10 MeV/c^2.
 
Aaronvan said:
On pp. 459 of Dark Sun: The Making of the Hydrogen Bomb Richard Rhodes writes:


He is talking about soft-x-rays in that quote. I understand that X-rays are massless so their weight is zero regardless of the density of the flux. Is this not correct? Is there a better comparison he could have used to describe the density of the X-ray flux?
Nuclear detonations release energy in a broad EM spectrum. One sees the bright visible portion of the spectrum, but there is infrared, visible, UV, X-ray and gamma ray. The nuclear fission produces prompt gamma rays, and some of the fission products release gammas and beta particles. The high energy fission products, gammas, betas and X-rays then ionize atoms in the plasma and atmosphere, and these in turn release infrared, visible, UV and X-ray.

Perhaps Rhodes is referring to the equivalent-mass of the energy as indicated by mfb, or perhaps he is thinking of the momentum of the photons.