Calculation of Velocity:

We know that

mvr = nh/2π; v = nh/2πmr

By substituting for r we get

v = 2πKZe2/nh

Where except n and Z all are constants

v = 2.18 x 108 Z/n  cm/sec

Further application of Bohr’s work was made, to other one electron species (Hydrogenic ion) such as He+ and Li2+. In each case of this kind, Bohr’s prediction of the spectrum was correct. 

Illustration:

The velocity of electron in the second orbit of He+  will be

(A)   2.18 x 106   m/s               (B)   1.09 x 106 m/s

(C)  4.36 x 106  m/s                (D)    None of these

Solution:

v,= voZ/n. Hence (A) is correct.

 
Illustration:

Calculate the velocity of an electron in Bohr’s first orbit of hydrogen atom

(Given r = 0.53 x 10–10 m)

Solution:

According to Bohr’s theory

mvr = nh/2π or v = nh/2πmr

r = 0.53 x 10–10m

n = 1, h = 6.62 x 10–34kg m2 s–1, m = 9.1 x 10–31 kg

v = 1x (6.62 x 10-34 kgm2s-1) / 2 x 22/7 x(9.1x 10-31kg ) x ( 0.53 x 10-10m)  = 2.18x 106 m/s

 
Illustration:

The velocity of e- in first Bohr’s orbit is 2.17 x 106 m/s. Calculate the velocity in 3rdorbit of He2+ ion.

Solution:

vn = voZ/n

Hence v = 2.19 x 106x2/3  = 1.45 x 106 m/s

Related Resources
Problems with Solutions

Problems with Solutions True and False Problem:...

Quantum Numbers

QUANTUM NUMBERS An atom contains large number of...

Atomic Models

ATOMIC MODELS We know the fundamental particles of...

Photoelectric Effect

PHOTOELECTRIC EFFECT Sir J.J. Thomson, observed...

Quantum Mechanical Model of Atom

QUANTUM MECHANICAL MODEL OF ATOM The atomic model...

Discovery of Electron

DISCOVERY OF ELECTRON: CATHODE RAYS During the...

Fundamental Particles

FUNDAMENTAL PARTICLES Atoms are made...

Shapes and Size of Orbitals

Pauli’s Exclusion Principle: According to...

Relation-Kinetic Energy and Wavelength

Relation between Kinetic Energy and Wavelength:...

Atomic Spectrum

ATOMIC SPECTRUM If the atom gains energy the...

Discovery of Proton

DISCOVERY OF PROTON: POSITIVE RAYS OR CANAL RAYS...

Wavelengths of Electromagnetic Radiations

Wavelengths of Electromagnetic Radiations:...

Atomic Structure Terms

ATOMIC TERM Nuclide: Various species of atoms in...

Hunds rule of Maximum Multiplicity

Hund’s Rule of Maximum Multiplicity: This...

Solved Questions of Atomic Structure Part I

Solved Questions of Atomic Structure Part I...

Limitations of Bohrs Theory

Merits of Bohr’s Theory: * The experimental...

Radius and Energy Levels of Hydrogen Atom

Radius and Energy Levels of Hydrogen Atom:...

Dual Character

Dual Character DUAL CHARACTER (PARTICLE AND WAVE...

Characteristics of Wave

Characteristics of Wave SOME IMPORTANT...

A-Scattering Experiment

A-Scattering Experiment Conclusions of...

Heisenbergs Uncertainty Principle

HEISENBERG’S UNCERTAINTY PRINCIPLE All...

Bohrs Atomic Model

BOHR’S ATOMIC MODEL Bohr developed a model...

Calculation of Energy of Electron

Calculation of Energy of an Electron: The total...

Hydrogen Atom

HYDROGEN ATOM If an electric discharge is passed...

Objective Questions of Atomic Structure

Objective Questions of Atomic Structure Problem:...

Derivation of Angular Momentum from de Broglie Equation

Derivation of Angular Momentum from de Broglie...

Plancks Quantum Theory

PLANCK’S QUANTUM THEORY When a black body is...

Rules for Filling of Electrons in Various Orbitals

RULES FOR FILLING OF ELECTRONS IN VARIOUS ORBITALS...

Discovery of Neutron

DISCOVERY OF NEUTRON After the discovery of...