A hydrogen atom makes a 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) A)2.56 μm B)1.54 μm C)2.05 μm D)3.07 μm

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Quizplus · Accepted Answer

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

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

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