1. -4/9x 2. -x 3. -x/9 4. -4x

Answer: 2. -x Key idea: for hydrogen-like ions E_n=-E₁(H) Z²/n² . For He^+ (Z=2), n=1: -x=-4E₀ , so E₀=x/4 . For mathrmBe³⁺ (Z=4), n=2: E=-E₀16/4=-4E₀=-x . Answer: -x , option 2.

Topic: Bohr model and its limitations· Atomic Structure

The energy of an electron in the ground state (n = 1) for He^+ ion is -x J, then that for an electron in n = 2 state for Be^3+ ion in J is :

1. \(-\frac{4}{9}x\)

2. \(-x\)

3. \(-\frac{x}{9}\)

4. \(-4x\)

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Answer: 2. \(-x\)

Key idea: for hydrogen-like ions \(E_n=-E_1(H)\,\dfrac{Z^2}{n^2}\).

For \(\mathrm{He^+}\) (Z=2), n=1: \(-x=-4E_0\), so \(E_0=x/4\).

For \(\mathrm{Be^{3+}}\) (Z=4), n=2: \(E=-E_0\dfrac{16}{4}=-4E_0=-x\).

Answer: \(-x\), option 2.

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The energy of an electron in the ground state (n = 1) for He^+ ion is -x J, then that for an electron in n = 2 state for Be^3+ ion in J is :

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