Atoms

Important Topics of Atoms

The chapter on Atoms describes the understanding of the atomic structure based on experimental observations and theoretical frameworks. The important topics focus on atomic spectra, energy quantisation, and Bohr's model, which form the foundation of modern atomic physics. These subjects are the key ones that can be clearly understood to pass the board exams, JEE Main, and NEET because the questions are usually concept-oriented with straightforward numbers.

1. Atomic Models

Atomic Models explain the various theoretical concepts introduced to explain the internal structure of an atom. This topic describes why scientists have come up with different models on the basis of experimental observations in order to understand how electrons and the nucleus are arranged. It points out shortcomings of previous ones and the necessity of new, better theories. The atomic models can be studied to explain the development of the atomic theory and the basis of contemporary atomic physics.

2. Rutherford’s Nuclear Model of the Atom

The Nuclear Model of the Atom proposed by Rutherford was proposed as a result of the famous alpha-particle scattering experiment. According to the topic, an atom comprises a compact nucleus that is positively charged with electrons rotating around the nucleus. It proved the atomic nucleus of the atom and contradicted the previous models. But it did not give an explanation of atomic stability and line spectra.

3. Bohr’s Model of the Hydrogen Atom

The Model of the Hydrogen Atom by Bohr presented the idea of quantized electrons energy levels. In this topic, the postulates of Bohr are explained, based on which electrons rotate in constant circular orbits without energy radiation. It is able to explain the stability of the hydrogen atom together with its emission spectrum. The model is one of the significant achievements in the field of atomic physics.

4. Energy Levels in an Atom

Energy Levels in an Atom refer to the discrete and fixed energies, which can be possessed as they rotate around the nucleus. According to this topic, electrons cannot possess arbitrary energies and may spontaneously change levels, absorbing or emitting energy. It is the foundation of the knowledge of atomic transitions and spectra. Quantisation of energy forms the basis of the modern atomic theory.

5. Spectral Lines and Atomic Spectra

Spectral Lines and Atomic Spectra provide insight into the current relation between the emission and absorption of radiation at given wavelengths by atoms. This topic describes emission and absorption spectra as experimental evidence of quantised energy levels. The elements are characterised by their distinct spectral pattern and behave as a fingerprint. The theory of Bohr is greatly supported by atomic spectra.

6. Hydrogen Spectrum

The Hydrogen Spectrum is a collection of discrete spectral lines caused by the release of radiation by hydrogen atoms. Various spectral series are described in this topic, including Lyman, Balmer, Paschen, Brackett and Pfund. It demonstrates how radiation of certain wavelengths is emitted by electron changes in levels of energy. This spectrum was important in the formation of atomic models.

7. Rydberg Formula

The Rydberg Formula is a mathematical formula that is applied in determining the wavelengths of spectral lines that are produced or absorbed by a hydrogen atom. The wavelength of radiation varies with the electronic changes between various levels of energy, which is explained by this topic. It presents the Rydberg constant as a quantity of atomic physics. Knowledge of the Rydberg formula is important in the study of the hydrogen spectrum and in the solution of numerical problems involving atomic transitions.

8. Energy of an Electron in a Hydrogen Atom

The energy of an Electron in a hydrogen atom describes the fact that the electron in a hydrogen atom can have only a discrete number of values of energy. The basis of this topic is the model developed by Bohr, indicating that the electron energy is determined by the number of orbits, and it does not change in a certain orbit. It gives the reason why the energy of an electron is negative, meaning that it is in a bound state in the atom. This concept is significant in explaining the stability of atoms and numerical problems dealing with the energy transitions.

9. Radius and Velocity of Electron in Hydrogen Atom

Radius and Velocity of Electron in Hydrogen Atom explain the change in the size of the orbit of the electron and the speed of the electron with the various energy levels in a hydrogen atom. In this topic, by following the Bohr model, it is explained that the orbital radius grows and the velocity of the electron decreases with the number of orbits. Mathematical expressions are derived to relate radius and velocity to the principal quantum number. It is significant to understand this concept because it is valuable in the analysis of the atomic structure and numerical problems in the Bohr model.

10. Limitations of Bohr’s Model

The drawback of the Bohr Model has been used to explain why the theory of Bohr only applies to the case of hydrogen-like atoms. The failure of the model to explain the spectrum of multi-electron atoms, fine structure and Zeeman effect is discussed in this topic. It points out contradictions to classical and quantum mechanics. Modern quantum theory was developed as a result of these limitations.

Important formulas of Atoms

The Significant Formulas of the Atoms Chapter is important in the study of the structure of the atoms and the behaviour of electrons inside them. They are mostly based on a model of the hydrogen atom proposed by Bohr, and are applied to find out such quantities like energy levels, radius, velocity of electrons and wavelengths of spectral lines. Regular practice of these formulas is essential for solving numerical problems in Class 12 board exams, JEE Main, and NEET.

1. Radius of Electron Orbit (Bohr Radius):

$
r_n=\frac{n^2 h^2 \varepsilon_0}{\pi m e^2}=n^2 a_0
$

where
$a_0=0.529 \AA $ (Bohr radius),
$n$ = principal quantum number.

2. Velocity of Electron in nth Orbit:

$v_n=\frac{e^2}{2 \varepsilon_0 h} \cdot \frac{1}{n}$

3. Energy of Electron in nth Orbit:

$
E_n=-\frac{13.6}{n^2} \mathrm{eV}
$

(Negative sign indicates a bound state)

4. Energy Difference Between Two Orbits:

$\Delta E=E_{n_2}-E_{n_1}= h\nu$

5. Wavelength of Spectral Line (Rydberg Formula):

$
\frac{1}{\lambda}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)
$

where

$
R=1.097 \times 10^7 \mathrm{~m}^{-1}
$

6. Momentum of Electron:

p = mv

7. Angular Momentum Quantisation:

Angular Momentum Quantisation

Atoms: Previous Year Questions

Past Year Questions on Atoms assist the students to be aware of the pattern of the exam and also to be aware of what was mostly examined in this chapter. The questions are primarily concerned with the model of Bohr, the hydrogen spectrum, the Rydberg formula, energy levels, and numerical problems of electron energy, radius, and velocity. By practising PYQs, conceptual clarity, numerical accuracy and confidence are improved. Regular revisions of last year's exams are very useful in the Class 12 board exams, JEE Main and NEET.

Question 1:

The first three spectral lines of $H$-atom in the Balmer series are given $\lambda_1, \lambda_2, \lambda_3$ considering the Bohr atomic model, the wave lengths of first and third spectral lines $\left(\frac{\lambda_1}{\lambda_3}\right)$ are related by a factor of approximately $x^{\prime} \times 10^{-1}$. The value of $x$, to the nearest integer, is $\_\_\_\_$

Solution:

For $1^{s t}$ line

$
\begin{aligned}
& \frac{1}{\lambda_1}=R z^2\left(\frac{1}{2^2}-\frac{1}{3^2}\right) \\
& \frac{1}{\lambda_1}=R z^2 \frac{5}{36} \ldots \ldots .(i)
\end{aligned}
$
For $3^{r d}$ line

$
\begin{aligned}
& \frac{1}{\lambda_3}=R z^2\left(\frac{1}{2^2}-\frac{1}{5^2}\right) \\
& \frac{1}{\lambda_3}=R z^2 \frac{21}{100}
\end{aligned}
$

(ii) $+(i)$

$
\frac{\lambda_1}{\lambda_3}=\frac{21}{100} \times \frac{36}{5}=1.512=15.12 \times 10^{-1}
$
$
x \approx 15
$

Question 2:

In the line spectra of the hydrogen atom, the difference between the largest and the shortest wavelengths of the Lyman series is $304 \AA$. The corresponding difference for the Paschen series in $\AA$ is $\_\_\_\_$.

Solution:

$
\lambda=\frac{\mathrm{c}}{\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right)}
$

for Lyman series

$
\begin{aligned}
& \lambda_1=\frac{c}{\frac{1}{1^2}-\frac{1}{\infty^2}}=c(n=\infty \text { to } n=1) \\
& \lambda_2=\frac{c}{\frac{1}{1^2}-\frac{1}{2^2}}=\frac{4 c}{3}(n=2 \text { to } n=1) \\
& \Delta \lambda=\lambda_2-\lambda_1=\frac{c}{3}=304 \AA \Rightarrow c=912 \AA
\end{aligned}
$
For paschen series

$
\begin{aligned}
& \lambda_1=\frac{c}{\frac{1}{3^2}-\frac{1}{\infty^2}}=9 c \quad(n=\infty \text { to } n=3) \\
& \lambda_2=\frac{c}{\frac{1}{3^2}-\frac{1}{4^2}}=\frac{144 c}{7}(n=4 \text { to } n=3) \\
& \Delta \lambda=\lambda_2-\lambda_1=\frac{144 c}{7}-9 c=\frac{81 c}{7}=\frac{81 \times 912}{7} \\
& =10553.14 \AA
\end{aligned}
$

Question 3:

A beam of electrons of energy E scatters from a target having an atomic spacing of $1 \AA$. The first maximum intensity occurs at $\theta=60^{\circ}$. Then $E$ (in $e V$ ) is $\_\_\_\_$ .
(Planck constant $\mathrm{h}=6.64 \times 10^{-34} \mathrm{Js}, 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}$, electron mass $\mathrm{m}=9.1 \times 10^{-} { }^{31} \mathrm{~kg}$ )

Solution:

$
\begin{aligned}
& \frac{1}{2} m v^2=E \\
& \Rightarrow p=\sqrt{2 E m} \quad \therefore \lambda=\frac{\mathbf{h}}{\sqrt{2 \mathbf{E m}}}
\end{aligned}
$
For the first maxima,

$
\begin{aligned}
& 2 \mathrm{~d} \sin \theta=\lambda \\
\Rightarrow & 2 \times 10^{-10} \times \frac{\sqrt{3}}{2}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{Em}}} \\
\Rightarrow & 2 \mathrm{Em}=\frac{\left(10^{10} \times \mathrm{h}\right)^2}{3} \\
\Rightarrow & E=\frac{\left(10^{10} \times \mathrm{h}\right)^2}{6 \mathrm{~m}_{\mathrm{e}} \times \mathrm{e}}(\mathrm{eV}) \\
\Rightarrow & E=50.47 \mathrm{eV}
\end{aligned}
$

Atoms in Different Exams

The chapter on Atoms is very crucial in Class 12 board exams and major competitive exams since it presents the basics of atomic structure and quantisation of energy. This chapter is a scoring and concept-building chapter because questions largely test knowledge of the Bohr model, the spectrum of hydrogen, and applications of numbers. The awareness of the exam-wise focus and weightage enables the students to prepare effectively.

Important Books and Resources for Class 12 Atoms

A combination of NCERT textbooks, reference guides and practice materials will help students excel in the chapter Atoms since they can get to know the theoretical and numerical concepts. They include some of the most important concepts in physics, like the Bohr model, Hydrogen spectrum, Rydberg formula, energy levels, and atomic transitions, some of the most common questions on board exams and even competitive exams such as JEE Main, JEE Advanced and NEET.

NCERT Resources for Atoms

The best and exam-oriented study material on the topic of learning about the atomic structure as required by the Class 12 Physics syllabus is the NCERT resources of the chapter on Atoms. The NCERT textbook and exemplar problems clearly explain concepts such as Bohr's model, hydrogen spectrum, energy levels, and Rydberg formula using standard definitions, diagrams, and numericals. The preparation of the Class 12 board exams, NEET, and JEE Main will require extensive preparation using NCERT materials since most of the questions in this chapter are directly NCERT-based.

• NCERT solutions for Class 12 Physics Chapter 12 Atoms
• NCERT Exemplar Class 12 Physics Solutions Chapter 12
• NCERT notes Class 12 Physics Chapter 12 Atoms

NCERT Subjectwise Resources

NCERT subject-wise materials are organised and syllabus-based learning content on various subjects, which assists students in developing a good conceptual basis. They consist of textbooks, exemplar problems, and solutions and can thus be very helpful in the preparation for the board exams and even competitive exams such as JEE and NEET.

Related Topics,

Practice Questions based on Atoms

Practice Questions on the Atoms Chapter help students strengthen their understanding of atomic structure and energy quantisation. These questions primarily concern the model of Bohr, the spectrum of hydrogen, the Rydberg formula, energy levels, and the numerical problems of electron energy, radius and velocity. Practice enhances clarity of concepts, accuracy in numbers and uses of formulas. It is very helpful to solve a wide variety of questions of both Class 12 board exams and competitive exams ,such as JEE Main and NEET.

Conclusion

The chapter Atoms provides a good conceptual framework of the atomic structure and the quantised energy of atoms. The students can build up a clear and conceptual understanding by constantly updating important concepts, important formulae, model explanations involving the Bohr theory, the energy levels, the atomic spectra and the hydrogen atom. This is a systematic preparation that develops confidence and is very effective in attaining good results in Class 12 board exams and also in competitive exams such as JEE Main and NEET.