Question

The energy of an electron in the ground state (n=1) for He⁺ ion is -xJ, then that for an electron in n=2 state for Be³⁺ ion in J is:

• A. -x
• B. \(-\frac{x}{9}\)
• C. -4x
• D. \(-\frac{4}{9}x\)

Answer 1

The Correct Option is A

The energy of an electron in a hydrogen-like atom is given by:
$E_n = -\frac{13.6Z^2}{n^2} \, eV$,
where $Z$ is the atomic number and $n$ is the energy level.
For
$He^+$, $Z = 2$, and for 
$Be^{3+}$, $Z = 4$.
The ratio of energies in the ground state and $n = 2$ for $Be^{3+}$ gives:
$\frac{E}{E} = \frac{x}{1} = -x$.