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Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Bohr's Model and Physics of the Atom

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

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

Determine the radius and energy of a

\text{He}^+

ion in the state

n = 4

.

Options

A $4.24 \text{ \AA}$ , $-3.4 \text{ eV}$
B $2.12 \text{ \AA}$ , $-6.8 \text{ eV}$
C $8.46 \text{ \AA}$ , $-0.85 \text{ eV}$
D $4.24 \text{ \AA}$ , $-0.85 \text{ eV}$

Correct answer

A. $4.24 \text{ \AA}$ , $-3.4 \text{ eV}$

Step-by-step solution

The radius of the

n

-th orbit for a hydrogen-like species is given by

r_n = 0.529 \times \dfrac{n^2}{Z} \text{ \AA}

For

\text{He}^+

,

Z = 2

and

n = 4

.

r_4 = 0.529 \times \dfrac{4^2}{2} = 0.529 \times 8 = 4.232 \text{ \AA} \approx 4.24 \text{ \AA}

The energy of the

n

-th orbit is given by

E_n = -13.6 \times \dfrac{Z^2}{n^2} \text{ eV}

E_4 = -13.6 \times \dfrac{2^2}{4^2} = -13.6 \times \dfrac{4}{16} = -3.4 \text{ eV}

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