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(A) The energy of an electron in a hydrogen-like species is given by the formula: $E_n = E_0 \frac{Z^2}{n^2}$,where $E_0$ is the ground state energy o

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$1:4$

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(A) The energy of an electron in a hydrogen-like species is given by the formula: $E_n = E_0 \frac{Z^2}{n^2}$,where $E_0$ is the ground state energy of hydrogen,$Z$ is the atomic number,and $n$ is the principal quantum number.For hydrogen in the ground state $(n=1, Z=1)$:$E_H = E_0 \frac{1^2}{1^2} = E_0$For $Be^{3+}$ in the first excited state $(n=2, Z=4)$:$E_{Be^{3+}} = E_0 \frac{4^2}{2^2} = E_0 \frac{16}{4} = 4E_0$The ratio of the energy of the electron in the ground state of hydrogen to the energy of the electron in the first excited state of $Be^{3+}$ is:Ratio $= \frac{E_H}{E_{Be^{3+}}} = \frac{E_0}{4E_0} = \frac{1}{4} = 1:4$

The ratio of the energy of the electrons in the ground state of hydrogen to the electrons in the first excited state of $Be^{3+}$ is:

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