Energy and radius of first Bohr orbit of He+ and Li2+are [Given RH = 2.18×10–18 J, a0 = 52.9 pm]

Answer

Hydrogen-like Ions: Energy and Radius

For hydrogen-like ions, the total energy and orbit radius are given by:

Total Energy:
E_n = -R_H Z² / n²

Orbit Radius:
r_n = a₀ n² / Z

Where:

• E_n is the energy of the electron
• R_H is the Rydberg constant (≈ 2.18 × 10^-18 J)
• Z is the atomic number
• n is the principal quantum number
• a₀ is the Bohr radius (≈ 52.9 pm)

Examples (for n = 1):

He⁺ (Z = 2):
E = -8.72 × 10^-18 J
r = 26.4 pm

Li²⁺ (Z = 3):
E = -19.62 × 10^-18 J
r = 17.6 pm

As the atomic number Z increases, the energy becomes more negative and the orbit radius decreases.

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