Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

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 = 1 .

Determine the radius and energy of a

\text{He}^+

ion in the state

n = 1

.

Options

A $1.058 \text{ \AA}$ , $-3.4 \text{ eV}$
B $0.265 \text{ \AA}$ , $-13.6 \text{ eV}$
C $0.529 \text{ \AA}$ , $-13.6 \text{ eV}$
D $0.265 \text{ \AA}$ , $-54.4 \text{ eV}$

Correct answer

D. $0.265 \text{ \AA}$ , $-54.4 \text{ eV}$

Step-by-step solution

The radius of the

n^{\text{th}}

Bohr orbit for a hydrogen-like species 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 = 1

,

r_1 = 0.529 \times \dfrac{1^2}{2} = 0.2645 \text{ \AA} \approx 0.265 \text{ \AA}

The energy of the

n^{\text{th}}

state for a hydrogen-like species is given by

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

For

\text{He}^+

in the state

n = 1

,

E_1 = -13.6 \times \dfrac{2^2}{1^2} = -13.6 \times 4 = -54.4 \text{ eV}

Practice Bohr's Model and Physics of the Atom on Quantrex Academy →

More from Bohr's Model and Physics of the Atom

The Bohr radius is given by a_0 = (ε_0 h^2)/(π m e^2) . Determine the dimensions of the… Concepts Of Physics MCQ Edition [Volume 2]Determine the wavelength of the radiation emitted by hydrogen during the transition from… Concepts Of Physics MCQ Edition [Volume 2]Determine the smallest wavelength of radiation that can be emitted by hydrogen. Concepts Of Physics MCQ Edition [Volume 2]Determine the wavelength of the radiation emitted by hydrogen during the transition from… Concepts Of Physics MCQ Edition [Volume 2]Determine the wavelength of the radiation emitted by hydrogen during the transition from… Concepts Of Physics MCQ Edition [Volume 2]Determine the smallest wavelength of radiation that can be emitted by He^+ . Concepts Of Physics MCQ Edition [Volume 2]Determine the smallest wavelength of radiation that can be emitted by Li^ ++ . Concepts Of Physics MCQ Edition [Volume 2]Calculate the Rydberg constant by substituting the values of the fundamental constants… Concepts Of Physics MCQ Edition [Volume 2] Full Bohr's Model and Physics of the Atom list All Concepts Of Physics MCQ Edition [Volume 2] PYQs