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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: $E_{n}=\left(-2.18 \times 10^{-18} \mathrm{~J}\right)\left(\frac{Z^{2}}{n^{2}}\right)$ 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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