What is An Atom: Atomic Models and Spectral Lines

Atoms are the basic building blocks of matter that retain the chemical properties of an element. An atom is composed of protons, neutrons and electrons. The number of protons in the nucleus of an atom is equivalent to its atomic number. CBSE board exam may ask basic definitions like this; however, the JEE Main exam will not ask such basic questions. In this case, you will need to know more detailed concepts.

The total number of protons and neutrons in an atom is called its mass number. Atoms combine through chemical bonds to form molecules. The chemical bonds between atoms may be ionic, covalent or metallic, based on the nature of the atoms involved.

From the NEET exam point of view, understanding alpha particle scattering is really important. Through the following points you will understand what is this scattering:

• Ernst Rutherford conducted Alpha-particle scattering, which led to the development of the nuclear model of an atom. Rutherford directed a beam of alpha particles, which are positively charged particles, at a thin foil.
• He placed a fluorescent screen around this gold foil to observe exactly where alpha particles landed after either passing through or getting deflected by the foil.
• Rutherford observed that most of the particles passed straight through the foil.
• However, some of the alpha particles were deflected at certain angles.
• A small number of alpha particles were deflected by a very large angle. Some of these particles bounced back toward the source.
• As most of the alpha particles passed through the gold foil, it was evident that the atom mostly had empty space.
• The large deflection of some alpha particles suggested that positive charge must be concentrated within the atom because like charges repel each other.
• Since very few alpha particles were deflected at large angles, it was indicated that positive charge is occupied within a very small volume of the atom.

On the basis of the alpha-particle scattering experiment, Rutherford proposed an atomic model called "Nuclear Model of the Atom". As per this model: 

• Atom has a central core called a nucleus that contains most of the mass of an atom and all of its positive charge. 
• The nucleus of an atom is very small compared to the overall size of an atom. 
• Electrons are negatively charged particles within an atom that orbit the nucleus at relatively larger distance. 
• Atom's size is determined by electrons since they define the space an atom will occupy. 
• Most of the space in an atom is empty, which explains why alpha particles passed through gold foil without deflection. 

Niels Bohr proposed Bohr's Model of the atom, which shows significant development in the understanding of atomic structure. As per this model:

• Electrons orbit the nucleus in specific, well-defined paths known as orbits. Bohr proposed that only certain orbits with specific radii are allowed.
• Every orbit corresponds to a specific energy level. The energy of an electron in an atom is quantised, which means it can only have certain discrete values. 
• The lowest energy level is known as the ground state, and higher energy levels are known as excited states.
• Electrons do not radiate energy while orbiting the nucleus, contrary to what classical electromagnetic theory has predicted. 
• An electron within a fixed orbit has fixed energy. This means the electron will not lose energy continuously and will not spiral into the nucleus.
• Electrons can move between orbits either by absorbing or emitting energy. When electron moves from lower energy to higher energy level, it absorbs energy. 
• On the other hand, when electron moves from higher energy to lower energy level, it emits energy.
• Energy emitted or absorbed as photons and energy of photon corresponds to difference in energy between the two levels.
• Bohr proposed that angular momentum of an electron within an orbit is quantised. 

Understanding the line spectra is important for those taking the JEE Main exam and IISER exam. The line spectra of Hydrogen atom is a series of discrete wavelengths of light emitted or absorbed by Hydrogen atoms as they undergo transition between different energy levels. This is a direct consequences of quantized nature of electron energy levels in atoms. 

• In hydrogen atom, electrons exist only in certain discrete energy levels. These levels are quantized which means they have specific and fixed values.
• Energy level of each level is given by  $E_n = - \frac{ 13.6 \text{ eV} }{n^2}$ . Here n is the principal quantum number (n = 1, 2, 3...) and is the energy of the n-th level.
• When an electron transitions from a higher energy level to a lower one, it emits photon with energy equal to the difference between the two levels. 
• On the other hand, when an electron absorbs a photon, it transitions from lower energy level to higher level. In this case, photon's energy matches the energy difference between levels.
• The energy of an emitted or absorbed photon is given by E = hν, where h is Planck's constant and  $\nu$ is the light frequency.
• λ=c/ $\nu$, where c is the speed of light.

Line spectra of hydrogen is divided into serveral series. Each series correseponds to transitions to specific lower energy level:

1. Lyman Series: This series is produced when electron in hydrogen atom transitions from higher energy level (n>1) to the lowest energy level (n = 1) level. These lines are in ultravoilet region of spectrum.

$$\text{Here:} n_1 =1, n_2 =2,3,4,\dots$$ $$\text{For Balmer series,} n_1 =2, n_2 =3,4,5,\dots$$ $$\text{For Paschen series,} n_1 =3, n_2 =4,5,6,\dots$$ $$\text{For Brackett series,} n_1 =4, n_2 =5,6,7,\dots$$ $$\text{For Pfund series,} n_1 =5, n_2 =6,7,8,\dots$$

2. Balmer series: This is a set of lines in the hydrogen atom's emission spectrum. This corresponds to electron transitions from higher energy levels (n>2) to the second energy level (n=2). These transitions result in emission of photons whose wavelength falls within visible light spectrum.
3. Paschen series: This set of spectrum lines is formed when electrons transition from higher energy levels (n>3) to the third energy level, i.e. n = 3. Spectral lines of Paschen series fall within the infrared region of the electromagnetic spectrum. 
4. Brackett Series: This is a set of spectral lines in the emission spectrum of hydrogen atom. These lines occur when an electron transitions from a higher energy level (n>4)to n=4 energy level. Brackett series' spectral lines are found in the infrared region of electromagnetic spectrum.
5. Pfund Series: This series is a set of spectral lines in which electrons transition from higher energy level (n>5) to the fifth energy level (n=5). Wavelengths of spectral lines in Pfund series fall in the infrared region of the electromagnetic spectrum.

De Broglie presented a hypothesis that any moving particle has an associated wave called as matter wave or the De Broglie wave. The wavelength of the De Broglie wave is denoted as λ. This wavelength is related to the momentum of the particle p by the following equation:

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

Here: 

h is the Planck’s constant

As per the Bohr's second postulate, the angle momentum L of the electron in stable orbit is quantized and can take only certain discrete values. The angular momentum is given by

$L = n \cdot \frac{h}{ 2 \pi }$

Here, n is an integer known as principal quantum number. 

In a stable orbit, the electron's matter wave must form a standing. This means, it must constructively interfere with itself as electron travels around the orbits. For this to be true, circumference of orbit must be an integer multiple of electron's De Broglie wavelength.

Mathmatically, 2πr=nλ

Let us substitute De Broglie's wavelength formula λ = h/p into the above equation to get:

$2 \pi r = n \left( \frac{h}{p} \right)$

On rearranging the above equation, we get:

$p \cdot r = n \cdot \frac{h}{ 2 \pi }$

Since angular momentum is L= p⋅r, the above equation will be: 

$L = n \cdot \frac{h}{ 2 \pi }$

In short, De Broglie's hypothesis explains why angular momentum of an electron in stable orbit is quantized.