a hydrogen electron is elevated from level 1 to level 2. another electron is elevated from level 2 to level…

Explanation:

Step1: Recall energy - level formula

The energy of an electron in a hydrogen - like atom is given by $E_n=-\frac{13.6}{n^2}\text{ eV}$, where $n$ is the principal quantum number.

Step2: Calculate energy change for level 1 to level 2

$\Delta E_{1\rightarrow2}=E_2 - E_1=-\frac{13.6}{2^2}-\left(-\frac{13.6}{1^2}\right)=-\frac{13.6}{4}+ 13.6=13.6\left(1 - \frac{1}{4}\right)=13.6\times\frac{3}{4}=10.2\text{ eV}$.

Step3: Calculate energy change for level 2 to level 4

$\Delta E_{2\rightarrow4}=E_4 - E_2=-\frac{13.6}{4^2}-\left(-\frac{13.6}{2^2}\right)=-\frac{13.6}{16}+\frac{13.6}{4}=13.6\left(\frac{1}{4}-\frac{1}{16}\right)=13.6\times\frac{3}{16}=2.55\text{ eV}$.

Step4: Compare energy changes

Since $10.2\text{ eV}>2.55\text{ eV}$, the transition from level 1 to level 2 requires more energy.

Answer:

level 1 to level 2