Multiple Choice
Which element has the electron configuration 1s2 2s2 2p6 3s1?
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10. Periodic Properties of the Elements
The Electron Configuration
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Which of the following wavelengths corresponds to the energy required to excite a hydrogen atom from the n=2 state to the n=5 state?
A
434 nm
B
4340 nm
C
397 nm
D
4340 Å
Verified step by step guidance1
Identify the initial and final energy levels for the hydrogen atom transition: initial level $n_i = 2$ and final level $n_f = 5$.
Use the energy level formula for hydrogen: $E_n = -13.6 \frac{1}{n^2}$ eV, where $n$ is the principal quantum number.
Calculate the energy difference $\Delta E$ between the two levels using $\Delta E = E_{n_f} - E_{n_i} = -13.6 \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$ eV.
Convert the energy difference $\Delta E$ to wavelength $\lambda$ using the relationship between energy and wavelength: $\Delta E = \frac{hc}{\lambda}$, where $h$ is Planck's constant and $c$ is the speed of light. Rearranged, this is $\lambda = \frac{hc}{\Delta E}$.
Calculate $\lambda$ in meters and convert it to nanometers (1 nm = $10^{-9}$ m) or angstroms (1 Å = $10^{-10}$ m) to compare with the given options and identify the correct wavelength.
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