Concepts Of Physics MCQ Edition [Volume 2]PhysicsBohr's Model and Physics of the Atom

Determine the radius and energy of a He ^+ ion in the state n = 4 .

Options

A4.24 , -3.4 eV
B2.12 , -6.8 eV
C8.46 , -0.85 eV
D4.24 , -0.85 eV

Correct answer

A. 4.24 , -3.4 eV

Step-by-step solution

The radius of the n -th orbit for a hydrogen-like species is given by r_n = 0.529 n^2 Z For He ^+ , Z = 2 and n = 4 . r₄ = 0.529 4^2 2 = 0.529 8 = 4.232 4.24 The energy of the n -th orbit is given by E_n = -13.6 Z^2 n^2 eV E₄ = -13.6 2^2 4^2 = -13.6 4 16 = -3.4 eV

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