A hydrogen atom makes a downward transition from the $n = 15$ state to the $n = 5$ state. Find the wavelength of the emitted photon. (c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19J, h = 6.626 × 10^-³⁴ J ? s)

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The energy of a hydrogen atom in the nth state is given by:$$E_n = -13.6 	ext{ eV} \left(\frac{1}{n^2}ight)$$The energy difference between the n = 15 and n = 5 states is:$$\Delta E = E_5 - E_{15} = -13.6 	ext{ eV} \left(\frac{1}{5^2} - \frac{1}{15^2}ight) = 1.89 	ext{ eV}$$The wavelength of the emitted photon is given by:$$\lambda = \frac{hc}{\Delta E} = \frac{(6.626 	imes 10^{-34} 	ext{ J s})(3.00 	imes 10^8 	ext{ m/s})}{1.89 	ext{ eV}(1.60 	imes 10^{-19} 	ext{ J/eV})} = 2.56 \mu	ext{m}$$

A Hydrogen Atom Makes a Downward Transition from The n=15n = 15n=15

A Hydrogen Atom Makes a Downward Transition from The $n = 15$