When a hydrogen atom going from $$n = 2$$ to $$n = 1$$ emits a photon, its recoil speed is $$\frac{x}{5}$$ m s$$^{-1}$$. Where $$x =$$ _______. (Use: mass of hydrogen atom $$= 1.6 \times 10^{-27}$$ kg, charge of electron $$e = 1.6 \times 10^{-19}$$ C)

Energy of photon (n=2→n=1): $$E = 13.6(1-1/4) = 10.2$$ eV $$= 10.2 \times 1.6 \times 10^{-19}$$ J.

Momentum: $$p = E/c = 10.2 \times 1.6 \times 10^{-19}/(3 \times 10^8) = 5.44 \times 10^{-27}$$ kg⋅m/s.

Recoil speed = $$p/m = 5.44 \times 10^{-27}/(1.6 \times 10^{-27}) = 3.4$$ m/s = $$17/5$$. $$x = 17$$.

The answer is $$\boxed{17}$$.