Using Bohr'S Postulates of the Atomic Model, Derive the Expression for Radius of Nth Electron Orbit - Physics


Using Bohr's postulates of the atomic model, derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohr's radius.



According to the postulates of Bohr’s atomic model, the electrons revolve around the nucleus only in those orbits for which the angular momentum is the integral multiple of `h/(2pi)`


Angular momentum is given by

L = mvr

According to Bohr’s 2nd postulate


n → Principle quantum

vn → Speed of moving electron in the nth orbit

rn→ Radius of nthorbit


`:.v_n=1/n e^2/(4piin_0) 1/((h/(2pi)))`

`:.r_n=(n^2/m)(h/(2pi))^2 (4piin_0)/e^2`

For n = 1 (innermost orbit),


This is the expression for Bohr's radius.

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2013-2014 (March) All India Set 2


An electron is orbiting in 5th Bohr orbit. Calculate ionisation energy for this atom, if the ground state energy is -13.6 eV.

Obtain an expression for the radius of Bohr orbit for H-atom.

State Bohr’s third postulate for hydrogen (H2) atom. Derive Bohr’s formula for the wave number. Obtain expressions for longest and shortest wavelength of spectral lines in ultraviolet region for hydrogen atom

Calculate the radius of second Bohr orbit in hydrogen atom from the given data.

Mass of electron = 9.1 x 10-31kg

Charge on the electron = 1.6 x 10-19 C

Planck’s constant = 6.63 x 10-34 J-s.

Permittivity of free space = 8.85 x 10-12 C2/Nm2

Find the frequency of revolution of an electron in Bohr’s 2nd orbit; if the radius and speed of electron in that orbit is 2.14 × 10-10 m and 1.09 × 106 m/s respectively. [π= 3.142]

What is the maximum number of emission lines when the excited electron of an H atom in n = 6 drops to the ground state?

What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is –2.18 × 10–11 ergs.

Draw a neat, labelled energy level diagram for H atom showing the transitions. Explain the series of spectral lines for H atom, whose fixed inner orbit numbers are 3 and 4 respectively.

How many electrons in an atom may have the following quantum numbers?

n = 4, `m_s =  -1/2`

How many electrons in an atom may have the following quantum numbers?

n = 3, l = 0

Calculate the energy required for the process 

\[\ce{He^+_{(g)} -> He^{2+}_{(g)} + e^-}\]

The ionization energy for the H atom in the ground state is 2.18 ×10–18 J atom–1

Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has a duration of 2 ns and the number of photons emitted during the pulse source is 2.5 × 1015, calculate the energy of the source.

The longest wavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate the frequency of each transition and energy difference between two excited states.

If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5 × 107 ms–1, calculate the energy with which it is bound to the nucleus.

The ratio of kinetic energy of an electron in Bohr’s orbit to its total energy in the same orbit  is

(A) – 1

(B) 2

(C) 1/2

(D) – 0.5

In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1.5 × 1011 m with orbital speed 3 × 104 m/s. (Mass of earth = 6.0 × 1024 kg)

if `E_p` and `E_k` represent potential energy and kinetic energy respectively, of an orbital electron, then, according to B9hr's theory:

a)`E_k = -E_p"/"2`

b) `E_k = -E_p`

c) `E_k = -2E_p`

d) `E_k = 2E_p`


Using Bohr’s postulates, obtain the expressions for (i) kinetic energy and (ii) potential energy of the electron in stationary state of hydrogen atom.

Draw the energy level diagram showing how the transitions between energy levels result in the appearance of Lymann Series.

Using Bohr’s postulates, obtain the expression for total energy of the electron in the nth orbit of hydrogen atom.

Balmer series was observed and analysed before the other series. Can you suggest a reason for such an order?

Suppose, the electron in a hydrogen atom makes transition from n = 3 to n = 2 in 10−8 s. The order of the torque acting on the electron in this period, using the relation between torque and angular momentum as discussed in the chapter on rotational mechanics is

Which of the following parameters are the same for all hydrogen-like atoms and ions in their ground states?

In a laser tube, all the photons

When a photon stimulates the emission of another photon, the two photons have
(a) same energy
(b) same direction
(c) same phase
(d) same wavelength

Evaluate Rydberg constant by putting the values of the fundamental constants in its expression.

A positive ion having just one electron ejects it if a photon of wavelength 228 Å or less is absorbed by it. Identify the ion.

According to Maxwell's theory of electrodynamics, an electron going in a circle should emit radiation of frequency equal to its frequency of revolution. What should be the wavelength of the radiation emitted by a hydrogen atom in ground state if this rule is followed?

Radiation coming from transition n = 2 to n = 1 of hydrogen atoms falls on helium ions in n = 1 and n = 2 states. What are the possible transitions of helium ions as they absorbs energy from the radiation?

A neutron moving with a speed υ strikes a hydrogen atom in ground state moving towards it with the same speed. Find the minimum speed of the neutron for which inelastic (completely or partially) collision may take place. The mass of neutron = mass of hydrogen = 1.67 × 10−27 kg.v

Radiation from hydrogen discharge tube falls on a cesium plate. Find the maximum possible kinetic energy of the photoelectrons. Work function of cesium is 1.9 eV.

Consider a neutron and an electron bound to each other due to gravitational force. Assuming Bohr's quantization rule for angular momentum to be valid in this case, derive an expression for the energy of the neutron-electron system.

Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of h/2π. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model?

State any two Bohr’s postulates and write the energy value of the ground state of the hydrogen atom. 

According to Bohr, 'Angular momentum of an orbiting electron is quantized'. What is meant by this statement?

If l3 and l2 represent angular momenta of an orbiting electron in III and II Bohr orbits respectively, then l3: l2 is :

Draw energy level diagram for a hydrogen atom, showing the first four energy levels corresponding to n=1, 2, 3 and 4. Show transitions responsible for:
(i) Absorption spectrum of Lyman series.
(ii) The emission spectrum of the Balmer series.

How are various lines of Lyman series formed? Explain on the basis of Bohr’s theory.

Write postulates of Bohr’s Theory of hydrogen atom.

Mention demerits of Bohr’s Atomic model.

The dissociation constant of a weak base (BOH) is 1.8 × 10−5. Its degree of dissociation in 0.001 M solution is ____________.

What is the energy in joules released when an electron moves from n = 2 to n = 1 level in a hydrogen atom?

The spectral line obtained when an electron jumps from n = 5 to n = 2 level in hydrogen atom belongs to the ____________ series.

A particle has a mass of 0.002 kg and uncertainty in its velocity is 9.2 × 10−6 m/s, then uncertainty in position is ≥ ____________.

(h = 6.6 × 10−34 J s)

The energy associated with the first orbit of He+ is ____________ J.

Which of the following is/are CORRECT according to Bohr's atomic theory?

(I) Energy is emitted when electron moves from a higher stationary state to a lower one.

(II) Orbits are arranged concentrically around the nucleus in an increasing order of energy.

(III) The energy of an electron in the orbit changes with time.

The radius of the third Bohr orbit for hydrogen atom is ____________.

In Bohr model of hydrogen atom, which of the following is quantised?

If the radius of first electron orbit in hydrogen atom be r then the radius of the fourth orbit ill be ______.

Using Bohr's postulates derive the expression for the radius of nth orbit of the electron.

Ratio of longest to shortest wavelength in Balmer series is ______.

Calculate the energy and frequency of the radiation emitted when an electron jumps from n = 3 to n = 2 in a hydrogen atom.

Derive an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n – 1). Also show that for large values of n, this frequency equals to classical frequency of revolution of an electron.

On the basis of Bohr's model, the approximate radius of Li++ ion in its ground state ifthe Bohr radius is a0 = 53 pm : 

According to the Bohr theory of H-atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as:

In form of Rydberg's constant R, the wave no of this first Ballmer line is

The wavelength of the first time line of Ballmer series is 6563 A°. The Rydberg constant for hydrogen is about:-

The angular momentum of electron in nth orbit is given by

The energy of an electron in hth orbit of hydrogen atom is –13.6/n2ev energy required to excite the electron from the first orbit to the third orbit is

According to Bhor' s theory the moment of momentum of an electron revolving in second orbit of hydrogen atom will be.

The ratio of the ionization energy of H and Be+3 is ______.

The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because ______.

A set of atoms in an excited state decays ______.

Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.

Given below are two statements:

Statements I: According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.

Statement II: According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increase with a decrease in principal quantum number.
In light of the above statements, choose the most appropriate answer from the options given below:

The value of angular momentum for He+ ion in the first Bohr orbit is ______.

The wavelength in Å of the photon that is emitted when an electron in Bohr orbit with n = 2 returns to orbit with n = 1 in H atom is ______ Å. The ionisation potential of the ground state of the H-atom is 2.17 × 10−11 erg.

The number of times larger the spacing between the energy levels with n = 3 and n = 8 spacing between the energy level with n = 8 and n = 9 for the hydrogen atom is ______.

An electron in H-atom makes a transition from n = 3 to n = 1. The recoil momentum of the H-atom will be ______.

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its (i) second permitted energy level to the first level. and (ii) the highest permitted energy level to the first permitted level.

A hydrogen atom in its first excited state absorbs a photon of energy x × 10-2 eV and exited to a higher energy state where the potential energy of electron is -1.08 eV. The value of x is ______.

In Bohr's atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:

According to Bohr atom model, in which of the following transitions will the frequency be maximum?

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, λ12, of the photons emitted in this process is ______. 

Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will therefore be proportional to:

If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is ______.

The first ionization energy of H is 21.79 × 10-19 J. The second ionization energy of He atom is ______ × 10-19J.

The line at 434 nm in the Balmer series of the hydrogen spectrum corresponds to a transition of an electron from the nth to second Bohr orbit. The value of n is ______.

A 100 eV electron collides with a stationary helium ion (He+) in its ground state and exits to a higher level. After the collision, He+ ions emit two photons in succession with wavelengths 1085 Å and 304 Å. The energy of the electron after the collision will be ______ eV.

Given h = 6.63 × 10-34 Js.

The energy of an electron in the first Bohr orbit of the H-atom is −13.6 eV. The energy value of an electron in the excited state of Li2+ is ______.

A hydrogen atom in is ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of ______.

(Given, Planck's constant = 6.6 × 10-34 Js)

What is the energy associated with first orbit of Li2+ (RH = 2.18 × 10-18)?

In hydrogen atom, transition from the state n = 6 to n = 1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition ______.

In Bohr's theory of hydrogen atom, the electron jumps from higher orbit n to lower orbit p. The wavelength will be minimum for the transition ______.

A 20% efficient bulb emits light of wavelength 4000 Å. If the power of the bulb is 1 W, the number of photons emitted per second is ______.

[Take, h = 6.6 × 10-34 J-s]

What is the energy of an electron in stationary state corresponding to n = 2?

According to Bohr's theory, the radius of the nth Bohr orbit of a hydrogen like atom of atomic number Z is proportional to ______.

Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is ______.

The total energy of an electron in the nth orbit of the hydrogen atom is proportional to ______.

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. If R is the Rydberg constant then the principal quantum number n of the excited state is ______.

An electron in a hydrogen atom has an energy of -3.4 eV. The difference between its kinetic and potential energy is ______.

Using Bohr’s Theory of hydrogen atom, obtain an expression for the velocity of an electron in the nth orbit of an atom.


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