# Atomic Structure Assignment Help

The Atom is a basic unit of matter that consists of a dense, central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons (except in the case of hydrogen-1, which is the only stable nuclide with no neutrons). The electrons of an atom are bound to the nucleus by the electromagnetic force. Likewise, a group of atoms can remain bound to each other, forming a molecule. An atom containing an equal number of protons and electrons is electrically neutral, otherwise it has a positive charge (electron deficiency) or negative charge (electron excess) and is an ion. An atom is classified according to the number of protons and neutrons in its nucleus: the number of protons determines the chemical element, and the number of neutrons determines the isotope of the element.

Atom structure:

Atom is defined as the very small particle. The atoms are having many chemical properties of the elements. The atoms structure are having the nucleus at its center. The electrons are also present in the atom. The electron is always surrounds the nucleus part. The particles like protons and neutrons are also present in the atom.

## Various Particles Present in the Diagram of an Atom Structure

The atom diagram structure consists of three types of particles. They are defined below the following,

1. Protons

2. Neutrons

3. Electrons

## Explanation for the Various Particles for the Diagram of Atom Structure

The diagram of an atom structure is shown below,

Protons:

The protons present in the atom are having a positive charge. The positive charge is equal to the negative charge present in the electrons. The number of particles present in the atoms is used for the representation of the atomic number. Protons are 1836 times greater than the electrons. The proton structure is discovered by the scientist named Ernest Rutherford.

• The mass of the proton is given by 938 MeV/c2 = 1.67 x 10-27 kg.
• The charge of the3 proton is given by 1.602 x 10-19 Coulombs.
• The diameter of the proton is given by 1.65 x 10-15 m.

Electron:

The electrons are having the negative charges. The electrons cannot able to split into the further particles. The electrons move freely in the diagram of an atom. The electron forms the electron clouds.

• The mass of an electron present in the atom is given by 9.2095 x 10-31 kg.
• The charge of an electron present in the atom is given by -1.602177 x 10-19 C.
• The electron rest energy present in the atom is given by 0.511 MeV.
• The spin of an electron present in the atom is given by + `(1)/(2)` or -`(1)/(2)`

Neutron:

The charge of the neutron present in the atom is having neutral charge. The neutrons present in the atom are used to represent the isotope of the element.

• The mass of the neutron is given by 1.67492729 × 10−27 kg.
• The charge of the neutron is given by 0.
• The spin of the neutron is given by `(1)/(2)`

## Introduction to Metal atomic structure:

Metals are large structures of atoms, in which these atoms are bonded to each other by strong metallic bonds.

In this atomic structure one metal is surrounded by the different number of atoms, the number of atom surrounded by particular atom is called as coordination number. Metal has 12, 8, 6 co-ordination number. 12 co-ordination number means one metal atom is surrounded by the 12 atoms. 8 means one metal atom is surrounded by 8 other atoms.

## Properties of Metals Depends on the Metal Atomic Structure

All the properties of metals are depends on the metal atomic structure.  The different properties of metals are given as follows:

Melting points and boiling points

The boiling and melting points of metals are very high. This is because of the strength of the metallic bond. The strength of metallic bond is different for different metals. It also depends on the number of electrons which each atom delocalizes into the ocean of electrons. It means that melting and boiling points depends on metal atomic structure.

The melting and boiling points of potassium and that of sodium are relatively low because of  each atom only has one electron to contribute towards the bond.

Electrical conductivity

The atomic structure of metals is responsible for this property, electrical conductivity. In three-dimensional space, the delocalized electrons of the metal are free to move and even they can cross boundaries. Liquid metals are also good conductor of electricity. Therefore, electrical conductivity of metal depends on metal atomic structure. This decides up to how much power any metal conduct electricity.

thermal conductivity

The atomic structure of metals also gives the information that metals are very good conductors of heat. The electrons pick up the heat energy as the additional kinetic energy and hence, the electrons move faster. Thus, the heat energy is to the whole metal by the movement of these electrons.

Malleability and ductility

Metals are termed as malleable, i.e., they can be beaten into thin sheets and ductile, i.e., they can be pulled out into thin wires. Atomic structure of metal can explain this property. Atoms in the metals can roll over one other into new positions with no breaking of any metallic bond.

## 1.)Bohr's Atomic Model

In 1913, Neils Bohr proposed a model of an atom based on the Planck's quantum theory of radiation. The basic postulates of Bohr's theory are:

• An atom consists of a small, heavily positively charged nucleus around which electrons revolve in definite circular paths called orbits.
• These orbits are associated with definite energies called energy shells/energy levels. They are designated as K, L, M, N, …. etc. shells or numbered as 1, 2, 3, 4, …..etc. from the nucleus.
• As long as the electron remains in a particular orbit /energy shell its energy remains constant. This accounts for the stability of an atom.
• Only those orbits are permitted in which angular momentum of the electron is a whole number multiple of    where h is Plancks constant. Any moving body taking a circular orbit has an angular momentum equal to the product of its mass (m), velocity of movement (v) and radius of orbit (r). In other words the angular momentum of an electron

Thus,

This postulate introduces the concept of quantization of angular momentum.

• Electrons can either lose or absorb energy abruptly, when they jump from one energy level to another. For instance when an electron moves from the 'normal or ground state - E1' of an atom i.e., the state of lowest energy as required by its 'n' and 'l' values, to a higher level, it causes the atom to be in its 'excited state - E2' i.e., where electrons in an atom occupy energy levels higher than those permitted by its 'n' and 'l' values. The reverse is also true and the change in energy is DE,

DE = E2 - E1 = hn

Fig: 3.13 - Energy changes in an electron jump

## Bohr's atomic model explained successfully:

• The stability of an atom. Bohr postulated that as long an electron remains in a particular orbit it does not emit radiation i.e. lose energy. Hence it does not become unstable.
• The atomic spectrum of hydrogen was explained due to the concept of definite energy levels. The one electron of hydrogen being closest to the nucleus is in its lowest energy shell (n =1) or normal ground state. It can absorb a definite amount of energy and jump to a higher energy state. This excited state being unstable, the electron comes back to a lower energy level.

When the energy emitted during transition, strikes a photographic plate, it gives its impression in the form of a line. This difference is also the energy of photon expressed as E2 - E1 = hn.

The frequency of the emitted radiation is:

Since E2 and E1 have only definite values and are characteristic of energy levels of atoms, the values of 'n' will also be definite and characteristic of the atoms. Thus each transition will produce a light of definite wavelength, which is observed as a line in the spectrum.

For example, if the electron jumps down from the third to the first energy level having energies E3 and E1 respectively, then the wavelength of the spectral line would be

Similarly, when the electron jumps down from the fourth to the first energy level having energies E4 and E1 respectively or from the fifth to the second i.e., E5 and E2, then we have

These will give different lines in the spectrum of the atom corresponding to different transitions having definite wavelengths.

• The sample of hydrogen gas contains a large number of atoms and when energy is supplied, the electrons in different hydrogen atoms absorb different amounts of energies. These are raised to different energy states. For example, the electrons in some atoms may jump to second energy level (L), while in others it may be to the third (M), fourth (N) or fifth (O) and so on. These electrons come back from the higher energy levels to the ground state in one or more jumps emitting different amount of energies.

Fig: 3.14 - Different routes to the ground state from n = 4

Different lines depending upon the difference in energies of the levels concerned can be summarized in the form of series named after the scientists who have discovered them.

Lyman series from n = 2, 3, 4, 5……to n = 1

Balmer series from n = 3, 4, 5, 6……to n = 2

Paschen series from n = 4, 5, 6, 7……to n = 3

Brackett series from n = 5, 6, 7, 8……to n = 4

Pfund series from n = 6, 7, 8, 9……to n = 5.
• The energy of the electron in a particular orbit of hydrogen atom could be calculated by Bohr's theory. The energy of the electron in the 'nth' orbit has been found to be

where 'm' is the mass and 'e' is the charge of the electron. The energy expression for hydrogen like ions such as He, Li can be written as:

where 'Z' is the nuclear charge, which is equal to atomic number.

Although Bohr's model successfully explained the stability and the line spectrum of hydrogen, it had its limitations. They were:

## Limitations and problems

• It could not explain the line spectrum of multi electron atoms.
• This model failed to explain the effect of magnetic field on the spectra of atoms (Zeeman effect).
• The effect of electric field on the spectra could not be explained by Bohr's model (Stark effect).
• The shapes of molecules arising out of directional bonding could not be explained.
• The dual nature of electrons (both as wave and particle) and the path of motion of the electron in well defined orbits were not correct.

## Problems

7. If the energy difference between the electronic states of hydrogen atom is 214.68 kJ mol-1, what will be the frequency of light emitted when the electron jumps from the higher to the lower energy state? (Planck's constant = 39.79 x 10-14 kJ mol-1)

## Solution

The frequency (n) of emitted light is related to the energy difference of two levels (DE) as

E = 214.68 kJ mol-1, h = 39.79 x 10-14 kJ mol-1

= 5.39 x 1014 s-1

8. The wavelength of first spectral line in the Balmer series is 6561 Å units. Calculate the wavelength of the second spectral line in Balmer series.

## Solution

According to Rydberg equation:

For the first line in Balmer series, n1 = 2, n2 = 3

For the second line in Balmer series, n1 = 2, n2 = 4

Dividing equations (i) by (ii)

## 2.)Quantum Mechanical Model of the Atom

Two new theories came to substantially modify Bohr's Atomic model. They are:

## Wave nature of material objects

In 1924, de Broglie's suggested that all material objects including an electron have a dual character; they behave as particles as well as waves. The wavelength associated with a particle of mass 'm', moving with velocity 'v' is given by de Broglie's relation as:

The discovery of the wave like character of the electron helped in the making of the modern electron microscope.

## Heisenberg's uncertainity principle

Heisenberg, in 1927 pointed out that it is not possible to measure simultaneously both the momentum (or velocity) and the position of a microscopic particle with absolute accuracy. Mathematically this may be expressed

Dp = uncertainity in momentum

The constant on the right side of the equation (the product of the two uncertainties) tells us that the two uncertainties are inversely related. If the momentum of the particle is measured with more accuracy there will be a large uncertainity in its position and vice versa.

Uncertainity is not due to the lack of refined techniques available, but because we cannot observe microscopic bodies without disturbing them. [Observations made as result of the impact of light suffer a change in the position or velocity of these microscopic objects]. This does not hold good for large objects of daily light, as the changes that occur are negligible.

## Probability picture of an electron

According to Heisenberg's uncertainty principle, it is impossible to describe the exact position of an electron at a given moment in terms of position, we can speak of most probable regions where the probability of finding an electron in the space around the nucleus of an atom is high. The electron does not always remain at a fixed distance from a nucleus. It keeps moving in the whole space around the nucleus but tends to remain most of the time within a small volume around the nucleus, where the probability of locating the electron is maximum.

A new atomic model, was needed to explain
• Wave nature (dual character) of atoms.
• The idea of uncertainity in the position of electrons in a atom.
• Concept of fixed energy states.
Schrodinger put the wave model or quantum mechanical model of atom forward. The behavior of an electron is defined by the mathematical representation:

where,

y = (psi) is a wave function of space coordinates 'x', 'y', 'z' and represents the amplitude of the electron wave.

m = mass of the electron

E = the total permissible energy level, which the electron can have.

V = potential energy of the electron given by ze2/r.

h = Planck's constant having the value 6.626 x 10-34 J s.

d= (delta)stands for infinitesimal change.

The wave length function y (psi) describes a number of possible states of an electron in an atom. Since a large number of solutions are possible, four quantum numbers were introduced, which describe meaningful permissible values of energy and location with respect to its nucleus.

## 3.)Quantum Numbers

Orbitals of electrons in atoms differ in size shape and orientation. Definite energies and angular movements characterize atomic orbitals. The state of an electron in any atom is defined by certain permissible values of energy and angular momentum, which describe its location with respect to its nucleus and its energy level. These permissible states are called orbitals and are expressed by a set of four numbers 'n', 'l', 'm' and 's' called quantum numbers. These numbers serve as the signature of the electrons, uniquely describing its position in the atom. The 'n', 'l' and 'm' indicate the spatial distribution while 's' indicates the spin orientation of the electrons.

## Principal quantum number

This quantum number determines the main energy shell or energy level in which the electron is present. The principal quantum number gives the average distance of the electron from the nucleus and energy associated with it.

It is denoted by the letter 'n' that can take whole number values starting from 1, 2, 3, 4, ….. . The shell with n = 1 is called first shell or 'K' shell. The shell with n = 2 is the 'L' shell and so on. The first shell is closest to the nucleus. As the value of 'n' increases, the distance from the nucleus as well as the energy of the electrons increases.

## Azimuthal quantum number or angular quantum number

The Azimuthal quantum number determines the angular momentum of the electron, denoted by the letter 'l'. The value of 'l' gives the sub level or sub shell in a given principal energy shell to which the electron belongs. It can have only positive integral values from zero to (n-1) where 'n' is the principal quantum number. The various sub shell values of l are also designated by the letters s, p, d, f,…… For any main energy level, the energies of the sub shell follow the order s > p > d > f.

The different sub shells are represented by first writing the value of 'n' and then the letter designated for the value of 'l'.

To illustrate,

n = 1 l = 0 one sub shell 1s

n = 2 l = 0,1 two sub shells 2s, 2p

n = 3 l = 0,1,2 three sub shells 3s, 3p, 3d

n =4 l = 0,1,2,3 four sub shells 4s, 4p, 4d, 4f

Thus for each value of 'n' there are 'n' values of 'l'.

The value of azimuthal quantum number gives the shape of the sub shell or orbital. So it is also called as orbital quantum number.

## Magnetic quantum number

The magnetic quantum number describes the behaviour of electron in a magnetic field. In the absence of external magnetic field electrons / orbitals having same values of 'n' and 'l' but different values on 'm' have the same energies. They are called degenerate orbitals. However, in the presence of an external magnetic field the orbitals vary in their energies slightly. This is because the preferred orientation of the orbital in space is a result of interaction of its own magnetic field with that of the external magnetic field.

It is denoted by the letter 'm' the values of which depends on 'l'. This quantum number can have all integral values from '-l' to '+l' including 0. Thus for given 'l' value there are (2l + 1) values of 'm'. Two orbitals in the same shell can have identical 'n' and 'l' values but they must have different fixed values of 'm'.

The number of orbitals in each sub shell are given below:

s sub shell l = 0 m = 0 only one orientation one orbital

p sub shell l = 1 m = +1,0, -1 three orientations three orbitals

d sub shell l = 2 m = +2,+1,0,-1,-2 five orientations five orbitals

## Spin quantum numbers

The orientation of spin of an electron is designated by its spin quantum number 's'. The spin orientation is an intrinsic characteristic of the electron connected more with its magnetic behaviour rather than rotation of an electron about its own axis. This number can have only two values corresponding to clockwise and anticlockwise spins i.e., +½ and -½. The clockwise spin is represented by an arrow (h) pointing upwards. The anti clockwise spin is represented by an arrow (i) pointing downwards. Each orbital can accommodate a maximum of two electrons provided they have opposite spins.

Fig: 3.15 - Number of subshells and orbitals in the K,L and M shells

## Problem

9.(a) What are the permissible values for l and m when n = 3?

(b) Which orbital is specified by l = 2 and n = 3?

## Solution

(a) For n = 3, the permissible values for 'l' and 'm' are: l = 0, 1, 2

For 'l' = 0 m = 0 (s-orbital)

## For 'l' = 1 m = +1, 0, -1 (p-orbital)

For 'l' = 2 m = +2, +1, 0, -1, -2 (d-orbital)

(b) For 'n' = 3 and 'l' = 2:

'l' = 2 means 'd' orbitals

The given orbital is '3d'.

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