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(Solved): In the Bohr model, the energy of an electron at a given energy level, \( B_{n} \), is described by ...




In the Bohr model, the energy of an electron at a given energy level, \( B_{n} \), is described by the equation:
\[
E_{n}=\le
In the Bohr model, the energy of an electron at a given energy level, \( B_{n} \), is described by the equation: \[ E_{n}=\left(-2.18 \times 10^{-18} \mathrm{~J}\right)\left(\frac{Z^{2}}{n^{2}}\right) \] where \( \mathrm{Z} \) is the number of protons in the nucleus of the atoms of that element, and \( n \) is a positive integer identifying the energy state (or "orbit" of the electron). The change in energy, \( \triangle \mathbf{E} \), for an electronic transition is therefore: \[ \Delta E=\left(-2.18 \times 10^{-18} J\right)\left(Z^{2}\right)\left(\frac{1}{n_{i}^{2}}-\frac{1}{n_{i}^{2}}\right) \] Common calculations involve converting between energy and frequency (Planck's relationship \( \mathrm{E}=\mathrm{h} v \), where \( \left.\mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right) \) and between frequency and wavelength \( \left(\mathrm{c}=\lambda \mathrm{v}, \mathrm{c}=3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right) \). calculate the wavelength of light emitted for the \( n_{1}=3 \) to \( n_{1}=2 \) transition. First, calculate the \( \Delta E \). Then, convert this to wavelength and express your answer in \( \mathrm{nm} \). Show your work.


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