$[-/1$ Points$]$

SERCP$1128\mathrm{.}3.$P$\mathrm{.}021.$MI$.$

$($a$)$ If an electron makes a transition from the $n=5$ Bohr orbit to the $n=3$ orbit, determine the wavelength of the photon created in the process.

nm

$($b$)$ Assuming that the atom was initially at rest, determine the recoil speed of the hydrogen atom when this photon is emitted.

$\frac{m}{s}$

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