The diagram shows different transitions across the energy levels for an electron in a certain atom. Among these, which transition represents the emission of a photon with the most energy?

Question

Aicharya · Accepted Answer

Since, energy, $E=13.6 Z^2\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)$
where, $Z$ is atomic number and $n$ is orbital number.
From given diagram,
$\begin{aligned}
& E_{\mathrm{I}}=13.6 Z^2\left(\frac{1}{3^2}-\frac{1}{1}\right)=-13.6 Z^2(0.88) \\
& E_{\mathrm{II}}=13.6 Z^2\left(\frac{1}{3^2}-\frac{1}{4^2}\right)=13.6 Z^2(0.049) \\
& E_{\mathrm{III}}=13.6 Z^2\left(\frac{1}{1^2}-\frac{1}{2}\right)=13.6 Z^2(0.75) \\
& E_{\mathrm{IV}}=13.6 Z^2\left(\frac{1}{2^2}-\frac{1}{4^2}\right)=13.6 Z^2(0.187)
\end{aligned}$
Here, $E_{\mathrm{III}}$ is highest.

The diagram shows different transitions across the energy levels for an electron in a certain atom. Among…

Solution