Which of the following relations is correct f | vedclass

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(B) The energy of an electron in a hydrogen-like species is given by the formula: $E_n = -13.6 	imes \frac{Z^2}{n^2} 	ext{ eV}$.For the ground state

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$E_1(H) = E_2(He^+) = E_3(Li^{2+}) = E_4(Be^{3+})$

Vedclass · Answer

(B) The energy of an electron in a hydrogen-like species is given by the formula: $E_n = -13.6 	imes \frac{Z^2}{n^2} 	ext{ eV}$.For the ground state of $H$ $(Z=1, n=1)$: $E_1 = -13.6 	imes \frac{1^2}{1^2} = -13.6 	ext{ eV}$.For the $n=2$ state of $He^+$ $(Z=2, n=2)$: $E_2 = -13.6 	imes \frac{2^2}{2^2} = -13.6 	ext{ eV}$.For the $n=3$ state of $Li^{2+}$ $(Z=3, n=3)$: $E_3 = -13.6 	imes \frac{3^2}{3^2} = -13.6 	ext{ eV}$.For the $n=4$ state of $Be^{3+}$ $(Z=4, n=4)$: $E_4 = -13.6 	imes \frac{4^2}{4^2} = -13.6 	ext{ eV}$.Thus,$E_1(H) = E_2(He^+) = E_3(Li^{2+}) = E_4(Be^{3+})$.

Which of the following relations is correct for the energy of the ground state of hydrogen-like species?

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