You think you have identified a new type of atom based on its atomic emission spectrum.Based on empirical data, it appears as though the energy levels of the atom are inversely proportional to N₂, like hydrogen.When an electron falls from n_initial = 5 to n_final = 2, a 1.4 *10^-18 J photon is emitted.What is the value of the Rydberg constant for this atom?

Question

Quizplus · Accepted Answer

The Rydberg formula for the energy levels of hydrogen-like atoms is given by $E = -R_H \left(\frac{1}{n_{final}^2} - \frac{1}{n_{initial}^2}\right)$, where $R_H$ is the Rydberg constant for hydrogen. Given that the energy of the emitted photon is $1.4 \times 10^{-18} J$ when an electron falls from $n_{initial} = 5$ to $n_{final} = 2$, we can rearrange the formula to solve for $R_H$: $R_H = \frac{E}{\left(\frac{1}{n_{final}^2} - \frac{1}{n_{initial}^2}\right)}$. Plugging in the given values, $R_H = \frac{1.4 \times 10^{-18} J}{\left(\frac{1}{2^2} - \frac{1}{5^2}\right)} = 6.7 \times 10^{-18} J$, which matches choice A.

You Think You Have Identified a New Type of Atom