When a hydrogen atom going from n = 2 to n = 1 emits a photon, its...

According to the above diagram, the difference in energy between the two states is given by

$\begin{cases}\Delta E & = & - 3 . 4eV - \left(- 13 . 6eV\right) \\ & = & 10 . 2eV\end{cases}$

The formula to calculate the recoil speed is given by

$v = \dfrac{∆ E}{mc} . . . \left(1\right)$

From equation (1), it follows that

$\begin{cases}v & = & \dfrac{10 . 2eV \times \dfrac{1 . 6 \times {10}^{- 19}J}{1eV}}{1 . 6 \times {10}^{- 27}kg \times 3 \times {10}^{8}m{s}^{- 1}} \\ & = & 3 . 4m{s}^{- 1} \\ & = & \dfrac{17}{5}m{s}^{- 1}\end{cases}$

Therefore, $x = 17$.