Structure of the Atom - Notes, Topics, Formula, Books, FAQs

The aspirant will also learn about Planck's quantum theory in which substance absorb or radiate energy discontinuously in the form of small packets. The phenomenon of the photoelectric effect in which there is the ejection of an electron from the surface of a metal when the light of suitable frequency strikes on its surface is something very interesting to know in this chapter. Following it an aspirant will come across four quantum numbers like the principal quantum number, azimuthal quantum number, magnetic quantum number and spin quantum number including the shape and size of different orbitals.

The shape of s orbital: (spherical)

The shape of p orbital:(dumbbell shaped)

The shape of the d orbital:

Rules for filling of electrons in various orbitals is a very important part to be studied in this chapter which will be helpful in the rest of the chemistry portion especially in inorganic and organic chemistry.

Rules For Filling Orbitals:

Rule 1 - Aufbau's principle - Lowest energy orbitals are filled first. Thus, the order of filling $1 \mathrm{~s}, 2 \mathrm{~s}, 2 \mathrm{p}, 3 \mathrm{~s}, 3 \mathrm{p}, 4 \mathrm{~s}, 3 \mathrm{~d}$, etc.

Rule 2 - Pauli Exclusion Principle - Only two electrons are permitted per orbital and they must be of opposite spin.

Rule 3- Hund's Rule - No pairing of electron starts in any of the degenerate orbitals until all orbitals of the subshell contain one electron each with parallel spin.

Quantum numbers:

They are the set of four numbers which explain the state of electron i.e., location, energy, type of orbital, orientation of orbital, etc. in an atom. Various quantum numbers are as follows:
1. Principal quantum number( $n$)
2. Azimuthal quantum number($l$)
3. Magnetic quantum number( $m$ )
4. Spin quantum number($s$)

Atomic structure formula:

1. The velocity of the electron in nth Bohr orbit:

$v=2.18 \times 10^8 \frac{Z}{n} \mathrm{~cm} / \mathrm{sec}$

2. The radius of nth Bohr orbital:

$r_n=0.529 \frac{n^2}{z} A^0$

3. The total energy of an electron in nth orbit:

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

4. The kinetic energy of electron: -(total energy of electron):

$13.6 \frac{Z^2}{n^2} \mathrm{eV}=-\mathrm{P} \cdot \mathrm{E} / 2$

5.The potential energy of the electron:

$-27.2 \frac{Z^2}{n^2} \mathrm{eV}$

6. Line Spectrum of Hydrogen-like atoms
$
\frac{1}{\lambda}=R Z^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)
$

Where R is called Rydberg constant, $R=1.097 * 10^7$ where $\mathrm{Z}=$ atomic number.

7. De-Broglie wavelength

$\lambda=\frac{h}{m v}=\frac{h}{p}$

How to prepare the atomic structure:

The first and foremost thing a candidate should do is to read the NCERT book and be thorough with all the topics covered in this chapter. In order to get away with the confusion of "How to prepare for atomic structure" the aspirant can also take the help of animation and videos which are easily available on the internet, to understand the shape of orbitals, photoelectric effect, Bohr's model and other related topics. It is very important to have a clear picture of the experimental setup and observations in the mind of the candidate. The candidate should also focus on the previous year's question papers related to atomic structure. Based on analysis, it is found that most of the numerical problems are from Bohr's theory and the hydrogen spectrum. These are important topics from exam point of view. So, the candidate should try to solve as many problems from these two topics.

Books for Atomic structure:

To prepare for atomic structure, these are some reference books that should be consulted;

1. J.DLee

2. O.P.Tandon

Some Solved Examples

Example 1: When an electron jumps from $n=4$ to $n=2$ then the change in angular momentum is approximately.
1) $1.1 \times 10^{-34} \mathrm{Js}$
2) (correct) $2.2 \times 10^{-34} \mathrm{Js}$
3) $3.3 \times 10^{-34} \mathrm{Js}$
4) $4.1 \times 10^{-34} \mathrm{Js}$

Solution

The angular momentum of the electron in any $\mathrm{n}^{\text {th }}$ Bohr Orbit is given by

$
\begin{aligned}
& m v r=\frac{n h}{2 \pi} \\
& \Delta L=4\left(\frac{h}{2 \pi}\right)-2\left(\frac{h}{2 \pi}\right)=\frac{h}{\pi} \\
& \Delta L=\frac{6.626 \times 10^{-34}}{3.14}=2.2 \times 10^{-34}
\end{aligned}
$
Hence, the answer is the option (2).

Example 2: Which of the following statements is incorrect for Bohr's model of an atom?

1) (correct) It is valid for a multi-electronic species

2) Angular momentum of an electron is quantized

3) The centripetal force of attraction required for circular motion is provided by the electrostatic force of attraction between the electron and the nucleus

4) Orbits have fixed energy and are referred to as stationary states

Solution

Bohr's model is valid for only electronic species.

All other given statements given in the options are correct.

Hence, the answer is the option (1).

Example 3: The de-Broglie wavelength of a particle of mass 6.63 g moving with a velocity of $100 \mathrm{~ms}^{-1}$ is:
1) (correct) $10^{-33} \mathrm{~m}$
2) $10^{-35} \mathrm{~m}$
3) $10^{-31} \mathrm{~m}$
4) $10^{-25} \mathrm{~m}$

Solution

As discussed in concept:
De-Broglie wavelength:

$
\begin{aligned}
& \lambda=\frac{h}{m v}=\frac{h}{p} \\
& \text { - wherein }
\end{aligned}
$

where $m$ is the mass of the particle
V: its velocity
p: its momentum
So,

$
\begin{aligned}
& \lambda=\frac{6.625 \times 10^{-34}}{6.63 \times 10^{-3} \times 100} \\
& \lambda=10^{-33} \mathrm{~m}
\end{aligned}
$

Hence, the answer is the option (1).

Example 4: The electronic configuration of copper is:

1) (correct) $[\operatorname{Ar}] 3 d^{10} 4 s^1$
2) $[\operatorname{Ar}] 3 d^9 4 s^2$
3) $[\operatorname{Ar}] 3 d^{10} 4 s^2$
4) $[\operatorname{Ar}] 3 d^8 4 s^2$

Solution
Ideally, the electronic configuration of Cu must be [Ar] $3 d^9 4 s^2$ but in this case, the electrons in d-orbitals are not symmetrically filled. Thus to maintain the symmetricity, one electron from the 4 s -orbital goes to the d-orbital and thus Cu maintains the electronic configuration as $[A r] 3 d^{10} 4 s^1$.

Hence, the answer is the option (1).

Conclusion

The presently accepted model for the structure of atoms is a natural outcome of earlier models, as over time scientists tried to overcome various shortcomings faced by earlier models. There is still a huge scope of research in this field as various particles like Quarks, Leptons, etc are discovered by researchers. These subatomic particles have many real-life applications. The revolutionary idea of Quantum Computer is also associated with these particles only.