The wavelength of an X-ray beam is 10 Å. The mass of a fictitious particle having the same energy as that of the X-ray photons is $$\frac{x}{3}h$$ kg. The value of $$x$$ is ______. ($$h$$ = Planck's constant)

The wavelength of the X-ray beam is $$\lambda = 10$$ Å $$= 10 \times 10^{-10}$$ m $$= 10^{-9}$$ m.

The energy of an X-ray photon is $$E = \frac{hc}{\lambda} = \frac{h \times 3 \times 10^8}{10^{-9}} = 3h \times 10^{17}$$ J.

For a fictitious particle with the same energy, using $$E = mc^2$$: $$m = \frac{E}{c^2} = \frac{hc/\lambda}{c^2} = \frac{h}{\lambda c}$$.

Substituting: $$m = \frac{h}{10^{-9} \times 3 \times 10^8} = \frac{h}{3 \times 10^{-1}} = \frac{10h}{3} = \frac{10}{3}h$$ kg.

Comparing with the given form $$\frac{x}{3}h$$ kg, we get $$x = 10$$.