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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 = 10 .

Determine the radius and energy of a

\text{He}^+

ion in the state

n = 10

.

Options

A $13.25 \text{ \AA}$ , $-1.088 \text{ eV}$
B $26.5 \text{ \AA}$ , $-0.136 \text{ eV}$
C $26.5 \text{ \AA}$ , $-0.544 \text{ eV}$
D $52.9 \text{ \AA}$ , $-0.136 \text{ eV}$

Correct answer

C. $26.5 \text{ \AA}$ , $-0.544 \text{ eV}$

Step-by-step solution

The radius of a hydrogen-like ion in the

n^{\text{th}}

state is given by:

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

For

\text{He}^+

, the atomic number

Z = 2

. For the state

n = 10

:

r_{10} = 0.529 \times \dfrac{10^2}{2} = 0.529 \times 50 = 26.45 \text{ \AA} \approx 26.5 \text{ \AA}

The energy of a hydrogen-like ion in the

n^{\text{th}}

state is given by:

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

For

\text{He}^+

in the state

n = 10

:

E_{10} = -13.6 \times \dfrac{2^2}{10^2} = -13.6 \times \dfrac{4}{100} = -0.544 \text{ eV}

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