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Energy Level - Bohr's Atomic Model - Practice Questions & MCQ

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Energy level for Hydrogen is considered one the most difficult concept.

  • Energy of electron in nth orbit is considered one of the most asked concept.

  • 71 Questions around this concept.

Solve by difficulty

As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion :

 Some energy levels of a molecule are shown in the figure.  The ratio of the wavelengths r=λ12, is given by :

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

Which of the following transitions in hydrogen atoms emit photons of highest frequency ?

The transition from the state n=4\; to\; n=3 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

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Which of the following atoms has the lowest ionization potential ?

Arrange the following electromagnetic radiations per quantum in the order of increasing energy :

A : Blue light      B : Yellow light
C : X-ray             D : Radiowave.


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The wavelengths involved in the spectrum of deuterium \left ( _{1}^{2} D\right ) are slightly different from that of hydrogen spectrum, because

The ratio of longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is:

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Out of the following which one is not a possible energy for a photon to be emitted by hydrogen atom according to Bohr,s atomic model?

Concepts Covered - 2

Energy of electron in nth orbit

Energy of electron in nth orbit

 Potential energy: An electron possesses some potential energy because it is found in the field of nucleus potential
energy of electron in n^{\text {th }} orbit of radius r_{n}  is given by:
U=k \cdot \frac{(Z e)(-e)}{r_{n}}=-\frac{k Z e^{2}}{r_{n}}

Kinetic energy : Electron posses kinetic energy because of it's motion. Closer orbits have greater kinetic energy than
outer ones. As we know \frac{m v^{2}}{r_{n}}=\frac{k \cdot(Z e)(e)}{r_{n}^{2}}

\text{Kinetic energy} \ K=\frac{k Z e^{2}}{2 r_{s}}=\frac{|U|}{2}

Total energy : Total energy E is the sum of potential energy and kinetic energy ie. E=K+U

\Rightarrow \quad E=-\frac{k Z e^{2}}{2 r_{n}}   also r_{n}=\frac{n^{2} h^{2} \varepsilon_{0}}{\pi n z e^{2}}

Hence E=-\left(\frac{m e^{4}}{8 \varepsilon_{0}^{2} h^{2}}\right) \frac{z^{2}}{n^{2}}=-\left(\frac{m e^{4}}{8 \varepsilon_{0}^{2} c h^{3}}\right) c h \frac{z^{2}}{n^{2}}

=-R \operatorname{ch} \frac{Z^{2}}{n^{2}}=-13.6 \frac{Z^{2}}{n^{2}} e V

\begin{array}{c}{\text { where } R=\frac{m e^{4}}{8 \varepsilon_{0}^{2} c h^{3}}=\text { Rydberg's constant }=1.09 \times 10^{7} \text { per }} \\ {m .}\end{array}


Energy level for Hydrogen

Energy level for Hydrogen

Ionization energy (IE): Total energy zero of a hydrogen atom corresponds to infinite separation between electron and nucleus. Total positive energy implies that the atom is ionized and electron is in unbound (isolated) state moving with certain kinetic energy. Minimum energy required to move an electron from ground state to n=\infty is called ionization energy of the atom or ion.

The formula for the ionisation energy is - 

                                                      E_{\text {ionisition }}=E_{\infty}-E_{n}=-E_{n}=\frac{13.6 Z^{2}}{n^{2}} \mathrm{eV}

On the basis of ionisation energy we can define the ionisation potential also - 

Ionization potential (IP): Potential difference through which a free electron must be accelerated from rest such that its kinetic energy becomes equal to ionization energy of the atom is called ionization potential of the atom.

                                                                        V_{\text {ionisation }}=\frac{E_{n}}{e}=\frac{13.6 Z^{2}}{n^{2}} \mathrm{V}

Now let us discuss Excitation energy and Excitation potential -

Excitation Energy and Excitation Potential
Now what is Excitation???

The process of absorption of energy by an electron so as to raise it from a lower energy level to some higher energy level is called excitation.

Excited state: The states of an atom other than the ground state are called its excited states. Examples are mentioned below -

\begin{array}{ll}{n=2,} & {\text { first excited state }} \\ {n=3,} & {\text { second excited state }} \\ {n=4,} & {\text { third excited state }} \\ {n=n_{0}+1,} & {n_{0} \text { th excited state }}\end{array}

Excitation energy -

Energy required to move an electron from ground state of the atom to any other excited state of the atom is called Excitation energy of that state.

                                                                        E_{excitation} = E_{higher } - E_{lower}

Excitation potential can also be defined on the basis of excitation energy. So the excitation potential is the potential difference through which an electron must be accelerated from rest so that its kinetic energy becomes equal to the excitation energy of any state is called excitation potential of that state. 

                                                                                 V_{excitation} = \frac{E_{excitation} }{e}

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Energy of electron in nth orbit
Energy level for Hydrogen

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Reference Books

Energy of electron in nth orbit

Physics Part II Textbook for Class XI

Page No. : 371

Line : 32

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