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

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

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

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

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 the nucleus potential energy of an electron in n^{\text {th }} orbit of the radius r_{n}  is given by
U=k \frac{(Z e)(-e)}{r_{n}}=-\frac{k Z e^{2}}{r_{n}}

Kinetic energy: Electrons possess kinetic energy because of their motion. Closer orbits have greater kinetic energy than
outer ones. As we know \frac{m v^{2}}{r_{n}}=\frac{k(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}}{z \pi m 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} m^{-1}}\end{array}

 

Energy level for Hydrogen

The energy level for Hydrogen

The energy of nth level of  hydrogen atom (z=1) is given as : \\ E_{n}=-\frac{z^{2 }13.6 }{n^{2}}eV=-\frac{13.6 }{n^{2}}eV \ \ \ \ \ \ (\because z=1)

\\ \text{Energy of Ground state}(n=1)= E_{1}=-\frac{13.6 }{1}eV=-13.6 eV \\ \text{Energy of first excited state}(n=2)= E_{2}=-\frac{13.6 }{4}eV=-3.4 eV \\ \text{Energy of second excited state}(n=3)= E_{3}=-\frac{13.6 }{9}eV=-1.51 eV \\ \text{Energy of third excited state}(n=4)= E_{4}=-\frac{13.6 }{16}eV=-0.85 eV

Binding Energy(B.E.) of nth orbit -Energy required to move an electron from nth orbit to n= \inftyis called the Binding energy of nth orbit

OR

Binding energy of nth orbit is the negative of the total energy of that orbit

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

Ionization energy (IE): Total energy of a hydrogen atom corresponds to infinite separation between electron and nucleus. Total positive energy implies that the atom is ionized and the electron is in an unbound (isolated) state moving with certain kinetic energy. The minimum energy required to move an electron from the ground state(n=1) to n=\infty is called the ionization energy of the atom or ion.

The formula for the ionization energy is - 

                                                      E_{\text {ionisition }}=E_{\infty}-E_{1}=-E_{1}={13.6 Z^{2}}\mathrm{eV}

On the basis of ionization energy, we can define the ionization 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 the ionization potential of the atom.

                                                                        V_{\text {ionisation }}=\frac{E_{Ionisation}}{e}={13.6 Z^{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 -

The energy required to move an electron from the ground state of the atom to any other excited state of the atom is called the 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 the excitation potential of that state. 

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

Study it with Videos

Energy of electron in nth orbit
Energy level for Hydrogen

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