A) For hydrogen, many electronic transitions from $n2$ to $n=2$ (Balmer series) emit photons which are in the visible range of the electromagnetic spectrum.
Demonstrate whether a photon emitted from the electronic transition $\mathrm{n}=3$ to $\mathrm{n}=2$ for the Li2+ ion is also in the visible range of the spectrum (i.e. between 400 and 700 nm).
B) Calculate the ionization energy for the remaining electron of Li2+.

Question

A) For hydrogen, many electronic transitions from $n>2$ to $n=2$ (Balmer series) emit photons which are in the visible range of the electromagnetic spectrum.
Demonstrate whether a photon emitted from the electronic transition $\mathrm{n}=3$ to $\mathrm{n}=2$ for the Li2+ ion is also in the visible range of the spectrum (i.e. between 400 and 700 nm).
B) Calculate the ionization energy for the remaining electron of Li2+.

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Use the Rydberg formula for hydrogen-like ions**: The wavelength of light emitted during electronic transitions can be calculated using the modified Rydberg formula for hydrogen-like ions: $ \lambda = \frac{n^2 h c Z^2}{R_H (n^2 - n_0^2)} $, where $n$ is the initial energy level, $n_0$ is the final energy level, $h$ is Planck's constant, $c$ is the speed of light, $Z$ is the atomic number, and $R_H$ is the Rydberg constant for hydrogen. ‖ ‖ 2 ⋮ **Calculate the wavelength for Li2+ transition**: For the Li2+ ion ($Z=3$), the transition is from $n=3$ to $n=2$. Plugging these values into the Rydberg formula gives us the wavelength of the emitted photon. ‖ ‖ 3 ⋮ **Determine if the wavelength is in the visible range**: Compare the calculated wavelength to the visible range of the electromagnetic spectrum (400 to 700 nm) to determine if the photon is visible. ‖ ∻A Answer∻ ⚹ [Insert final answer for Problem A here] ⚹ ∻Key Concept∻ ⚹ Rydberg formula for hydrogen-like ions ⚹ ∻Explanation∻ ⚹ The Rydberg formula is used to calculate the wavelength of emitted photons during electronic transitions in hydrogen-like ions. ⚹ ‖ 1 ⋮ **Use the ionization energy formula for hydrogen-like ions**: The ionization energy for a hydrogen-like ion can be calculated using the formula: $E = \frac{Z^2 R_H h c}{n^2}$, where $Z$ is the atomic number, $R_H$ is the Rydberg constant for hydrogen, $h$ is Planck's constant, $c$ is the speed of light, and $n$ is the principal quantum number of the electron being removed. ‖ ‖ 2 ⋮ **Calculate the ionization energy for Li2+**: For the Li2+ ion ($Z=3$) with the electron in the ground state ($n=1$), plug these values into the formula to find the ionization energy. ‖ ∻B Answer∻ ⚹ [Insert final answer for Problem B here] ⚹ ∻Key Concept∻ ⚹ Ionization energy for hydrogen-like ions ⚹ ∻Explanation∻ ⚹ The ionization energy formula is used to calculate the energy required to remove an electron from a hydrogen-like ion. ⚹◊What is the formula to calculate the ionization energy for the remaining electron of Li$^2$+ ion?⍭ Generate me a similar question◊

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