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Bohr Model Of The Hydrogen Atom - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Radius of orbit and velocity of electron is considered one the most difficult concept.

  • Bohr's Model of hydrogen atom is considered one of the most asked concept.

  • 93 Questions around this concept.

Solve by difficulty

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

In the Bohr model of the hydrogen atom, the orbital frequency of the electron depends on the principal quantum number as :

What is the angular momentum of an electron in the lowest energy level of a hydrogen atom:

 

Bohr's Model states that:-

The Bohr model for the spectra of a H-atom
A. will not apply to hydrogen in the molecular form.
B. will not be applicable as it is for a He-atom.
C. is valid only at room temperature.
D. predicts continuous as well as discrete spectral lines.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only.
Reason R : The formulation of Bohr model does not include repulsive force between electrons.

In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements :
Statement (I): The dimensions of Planck's constant and angular momentum are same.
Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.

In the light of the above statements, choose the most appropriate answer from the options given below.

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The radius of the second Bohr orbit of a singly ionised helium atom is

Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius 5th  orbit of the electron in Li2+ and He+is
 

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Concepts Covered - 2

Bohr's Model of hydrogen atom

Bohr's Model of hydrogen atom:  

Bohr proposed a model for hydrogen atom which is also applicable for some lighter atoms in which a single electron revolves around a stationary nucleus of positive charge Ze (called hydrogen-like atom)
Bohr's model is based on the following postulates-
(1). Bohr's first postulate was that an electron in an atom could revolve in certain stable orbits without the emission of radiant energy, contrary to the predictions of electromagnetic theory. According to this postulate, each atom has certain definite stable states in which it can exist, and each possible state has definite total energy. These are called the stationary states of the atom

For electrons revolving in a stable orbit, the necessary centripetal force is provided by the coulomb's force

mvn2rn=kze2rn2

(2) Bohr's second postulate defines these stable orbits. This postulate states that the electron revolves around the nucleus only in those orbits for which the

 angular momentum is some integral multiple of h2π where h is

the Planck's constant (= 6.6×1034 J s ). Thus the angular momentum (L) of the orbiting electron is quantised. That is

L=mvnrn=nh2π;n=1,2,3

(3) Bohr's third postulate incorporated into atomic theory the early quantum concepts that had been developed by Planck and Einstein. It states that an electron might make a transition from one of its specified non-radiating orbits to another of lower energy. When it does so, a photon is emitted having energy equal to the energy difference between the initial and final states. The frequency of the emitted photon is then given by

hν=EiEf

Ei is the energy of the initial state and Ef is the energy of the final state. Also, Ei > Ef.
rn-radius of the nth orbit
vn - speed of an electron in the nth orbit

Radius of orbit and velocity of electron

Radius of orbit and velocity of the electron

Radius of the orbit: For an electron around a stationary nucleus the electrostatic force of attraction provides the necessary centripetal force. 

ie. 14πε0(Ze)er2=mv2r (i)
also mvr=nh2π
From equations (i) and (ii) radius of r orbit

rn=n2h24π2kZme2=n2h2ε0πmZe2=0.53n2ZA(k=14πε0)rnn2Zrn=0.53n2ZÅ
Speed of electron: 

From the above relations, the speed of electrons in nth orbit can be calculated as

vn=2πkZe2nh=Ze22ε0nh=(c137)Zn=2.2×106Zn m/sec

where (c= speed of light =3×108 m/s)

Study it with Videos

Bohr's Model of hydrogen atom
Radius of orbit and velocity of electron

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