Atomic Structure

INTRODUCTION

The word .atom has been derived from the Greek word atomio which means .un-cutable or non-divisible.

DALTON’S ATOMIC THEORY

The matter is composed of small indivisible particles called atoms (from Greek word atomio, meaning indivisible). In 1808 Dalton proposed the following theory

1. Matter consists of atoms, which cannot be divided further.

2. All the atoms of a given element have identical mass. Atoms of different elements differ in mass.

3. Atoms combine in a fixed ratio to form Compounds.

4 The atoms cannot be created or destroyed.

SUCCESS OF DALTON’S ATOMIC THEORY

1. Atoms are the smallest part of matter
2. Atoms cannot be created of destroyed
3. Atoms of same element are similar in mass
4. Atoms combine with each other in simple ratios.

FAILURES OF DALTON’S ATOMIC THEORY

It could explain lows of chemical combination, as on today we know that all four points are not correct.

CATHODE RAYS

 CATHODE RAYS ARE NEGATIVELY CHARGED

 CATHODE RAYS TRAVEL IN STRAIGHT LINE.

CATHODE RAYS ARE PARTICLES

CHARGE /MASS (E/M) RATIO 

In 1897 JJ. Thomson determined the e/m value of cathode rays.

Thomson proved that e/m ratio is same, whatever material is of plates or gas filled in the tube

Ex.:  Which of the following is never true for cathode rays? 

1. They possess kinetic energy
2. They are electromagnetic waves
3. They produce heat
4. They produce mechanical pressure          Answer (c)

 MILLIKAN’S OIL DROP EXPERIMENT

 MASS OF ELECTRON

From Millikan's oil drop experiment e = 1.6022 x 10^-19 coulombs

   

 

 

ANODE RAYS

 

The smallest and lightest positive ion was obtained from hydrogen and was called proton. This characterized in 1919.

Later the presence of electrically neutral particle was found in the atom. These particles were discovered by Chadwick (1932) by bombarding a thin sheet of beryllium by α-particles, then electrically neutral particles having a mass slightly greater than that of the protons was emitted. He named these particles as neutrons.

Thomson Model of Atom

Plum pudding model OR

Water melon model 

 FUN FACTS JJ THOMSON (NOBEL PRIZE IN 1906)

 RUTHERFORD MODEL

Observations from a - particles scattering experiment by Rutherford:

a. Most of the a - particles (nearly 99 %) passed through gold foil undeflected

b. A small fraction of a- particles got deflected through small angles

c. Very few a - particles did not pass through foil but suffered large deflection nearly 180^O

Inferences Rutherford drew from  - particles scattering experiment:

a. Since most of the a -particles passed through foil undeflected, it means most of the space in atom is empty

b. Since some of the a -particles are deflected to certain angles; it means that there is positively mass present in atom

c. Since only some of the a -particles suffered large deflections; the positively charged mass must be occupying very small space

d. Strong deflections or even bouncing back of a -particles from metal foil were due to direct collision with positively charged mass in atom

As per Rutherford the size of nucleus is 10⁴-10⁵ times smaller than atom. Mardsen & Rutherford calculated density of nucleus.

Volume of atom / Volume of nucleus = 10¹⁵

Volume of earth approximately 1.08x10²¹ cubic meters

If earth was an atom then volume of nucleus = 1.08x10²¹/10¹⁵ = 1.08x10⁶

That is ball of radius = 44m

Rutherford and Marsden gave an equation to find radius of nucleus of any atom.

R = R_O A^1/3

Ro = 1.33x 10^-13 cm

A = no. of nucleons (Neutrons + protons)

Example calculate the density of nucleus of oxygen atom.

 

 

   =1.685 x 10¹⁴ gm. /cm³ = 1.685 x 10¹⁷ kg/m³

Mass of moon = 7.34767309 × 10²² kilograms

If moon is all made of nucleus it will become a ball of radius 32m. Slightly bigger than basketball court!!!!!!!

Drawback of Rutherford model

1. According to Rutherford’s model of atom, electrons which are negatively charged particles revolve around the nucleus in fixed orbits. Thus, the electrons undergo acceleration. According to electromagnetic theory of Maxwell, a charged particle undergoing acceleration should emit electromagnetic radiation. Thus, an electron in an orbit should emit radiation. Thus, the orbit should shrink. But this does not happen.

   2. The model does not give any information about how electrons are distributed around nucleus and what are energies of these electrons

Atomic number (Z): It is equal to the number of protons in an atom. It is also equal to the number of electrons in a neutral atom.

Mass number (A): It is equal to the sum of protons and neutrons.

Isotopes: These are the atoms of the same element having the same atomic number but different mass number. Ex ₆C¹² and ₆C¹⁴

Isobars: Isobars are the atoms of different elements having the same mass number but different atomic number. ₁₈Ar⁴⁰ and ₂₀Ca⁴⁰

Isoelectronic species: These are those species which have the same number of electrons. Ex. N₂ and CO

Isotones: Two nuclides are called isotones if they have same neutron number N, but different proton numbers Z. For example, Boron- 12 and Carbon-13 nuclei, but both contain 7 neutrons

ELECTROMAGNETIC WAVES

The radiations which are associated with electrical and magnetic fields are called electromagnetic radiations. When an electrically charged particle moves under acceleration, alternating electrical and magnetic fields are produced and transmitted. These fields are transmitted in the form of waves. These waves are called electromagnetic waves or electromagnetic radiations.

PROPERTIES OF ELECTROMAGNETIC RADIATIONS:

a. Oscillating electric and magnetic field are produced by oscillating charged particles. These fields are perpendicular to each other and both are perpendicular to the direction of propagation of the wave.

b. They do not need a medium to travel. That means they can even travel in vacuum.

WAVE NATURE OF ELECTROMAGNETIC RADIATION

Characteristics of electromagnetic radiations:

a. Wavelength: It may be defined as the distance between two neighbouring crests or troughs of wave as shown. It is denoted by l.

b. Frequency (n): It may be defined as the number of waves which pass through a particular point in one second.

c. Velocity (v): It is defined as the distance travelled by a wave in one second. In vacuum all types of electromagnetic radiations travel with the same velocity. Its value is 3 X10⁸ m sec^-1. It is denoted by v

d. Wave number: Wave number (ν  ) is defined as the number of wavelengths per unit length.

Relationship between velocity, frequency and wavelength Velocity = frequency x wavelength

Velocity = frequency x wavelength

THE SPECTRUM OF ELECTROMAGNETIC RADIATION

Ex.-The Vividh Bharati station of All India Radio, Delhi, broadcasts on a frequency of 1,368 kHz (kilo hertz).

Calculate the wavelength of the electromagnetic radiation emitted by transmitter. Which part of the electromagnetic spectrum does it belong to?

        

        = 219.3m

This is a characteristic radio wave wavelength.

Ex.: Calculate (a) wave number and (b) frequency of yellow radiation having wavelength 5800 Å.

Solution

1. Calculation of wavenumber

      λ = 5800Ǻ = 5800 x 10^-8 cm

                       = 5800 x 10^-10 m

      = 1.724 x 10⁶ m^-1

      = 1.724 x 10⁴ cm^-1

(b) Calculation of the frequency (n)

TYPES OF SPECTRUM (CAN BE CLASSIFIED IN TWO DIFFERENT WAYS

FIRST CLASSIFICATION SPECTRUM IS OF TWO TYPES: CONTINUOUS AND LINE SPECTRUM

a. The spectrum which consists of all the wavelengths is called continuous spectrum.

b. A spectrum in which only specific wavelengths are present is known as a line spectrum. It has bright lines with dark spaces between them.

Electromagnetic spectrum is a continuous spectrum. It consists of a range of electromagnetic radiations arranged in the order of increasing wavelengths or decreasing frequencies. It extends from radio waves to gamma rays.

SPECTRUM IS ALSO CLASSIFIED AS EMISSION AND ABSORPTION SPECTRUM.

• Emission spectrum: A substance absorbs energy and moves to a higher energy state. The atoms, molecules or ions that have absorbed radiation are said to be excited. Since the higher energy state is unstable they return to the more stable energy state by emitting the absorbed radiation in various regions of electromagnetic spectrum. The spectrum of radiation emitted by a substance that has absorbed energy is called an emission spectrum.
• Absorption spectrum is the spectrum obtained when radiation is passed through a sample of material. The sample absorbs radiation of certain wavelengths. The wavelengths which are absorbed are missing and come as dark lines

 

BOHR’S MODEL FOR HYDROGEN ATOM

a. An electron in the hydrogen atom can move around the nucleus in a circular path of fixed radius and energy. These paths are called orbits or energy levels. These orbits are arranged concentrically around the nucleus.

b. As long as an electron remains in a particular orbit, it does not lose or gain energy and its energy remains constant.

c. When transition occurs between two stationary states that differ in energy, the frequency of the radiation absorbed or emitted can be calculated. n = DE/h = (E₂-E₁)/h

n= Frequency of radiation

h = Planck's constant

E₁ Energy of lower energy state

E₂ Energy of higher energy state

d. An electron can move only in those orbits for which its angular momentum is an integral multiple of h/2p      Þ m_evr = n   where n = 1, 2 ,3 ….

Bohr’s theory for hydrogen atom:

a. Stationary states for electron are numbered in terms of Principal Quantum numbered as n=1, 2, 3…

b. For hydrogen atom: The radii of the stationary states is expressed as r_n = n²a₀ where a₀= 52.9 pm

c. Energy of stationary state E_n = -R_H  where n 1, 2,3,.... and R_H is 2.18x10^-18 ( rhydberg’s constant)

 CALCULATION OF WAVELENGTH FOR HYDROGEN SPECTRUM

 BOHR MODEL OF THE HYDROGEN ATOM

 

 

For equilibrium Þ centripetal force = centrifugal force

 

q₁ = Ze   q₂ = e

 

On solving equation (1) & (3)

 

 

From equation (3)

Þ  r_n = r₁ x n²                   Different orbit Some Atom (DOSA)

                     Same Orbit Different Atom (SODA)

From equation (4)

Þ  V_n = V₁ / n                   DOSA

Þ V_Z   = V_H x Z                SODA

Total Energy = K.E. + P.E.

 

Putting value form equation (3) & (4)

 

From equation (5)

                             D.O.S.A

                          S.O.D.A

For Hydrogen Atom Z    =1

As per Bohr model

∆E = hv

 

 

 

R_H=109677 cm^-1 and is called Rydberg’s constant

SUCCESS AND FAILURES OF BOHR’S MODEL OF ATOM

Success of Bohr’s model

1. The frequencies of spectrum in hydrogen lines were successfully explained.

2. The value of Rydberg’s constant calculated matched the experimental value.

3. It could explain the spectrum of hydrogen like species like He⁺, Li⁺² etc

LIMITATIONS OF BOHR’S MODEL OF ATOM

1. 1. Bohr’s model failed to account for the finer details of the hydrogen spectrum. For instance splitting of a line in the spectrum into two closely spaced lines.
   2. Bohr’s model was also unable to explain spectrum of atoms containing more than one electron.
   3. Bohr’s model was unable to explain Zeeman Effect i.e. splitting of spectral line in presence of magnetic effect.
   4. Bohr’s model also failed to explain Stark effect i.e. splitting of spectral line in presence of electric field.
   5. Bohr’s model could not explain the ability of atoms to form molecules by chemical bonds

Black body: An ideal body, which emits and absorbs all frequencies, is called a black body. The radiation emitted by such a body is called black body radiation.

Planck’s Quantum Theory

Planck said that atoms and molecules could emit (or absorb) energy only in discrete quantities and not in a continuous manner, a belief popular at that time.

Planck gave the name quantum to the smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation.

E µ n    Þ  E = hn Þ

The proportionality constant, ’h’ is known as Planck’s constant and has the value 6.626 10^-34 Js.     

PHOTOELECTRIC EFFECT

Experimental results observed for the experiment of Photoelectric effect observed by Hertz:

a. When beam of light falls on a metal surface electrons are ejected immediately i.e. there is not time lag between light striking metal surface and ejection of electrons

b. Number of electrons ejected is proportional to intensity or brightness of light

c. Threshold frequency ( n_o ): For each metal there is a characteristic minimum frequency below which photoelectric effect is not observed. This is called threshold frequency.

d. If frequency of light is less than the threshold frequency there is no ejection of electrons no matter how long it falls on surface or how high is its intensity.

Photoelectric work function (W_o): The minimum energy required to eject electrons is called photoelectric work function. W_o= h n_o

Energy of the ejected electrons: ½ m_ev² = h(n-n_o)

 The kinetic energies of these electrons increase with the increase of frequency of the light used. All the above results could not be explained on the basis of laws of classical physics.

Photoelectric work function (W_o): The minimum energy required to eject electrons is called photoelectric work function. W_o= h n_o

Energy of the ejected electrons: ½ m_ev² = h(n-n_o)

DUAL BEHAVIOUR OF ELECTROMAGNETIC RADIATION

It is concluded from active experiment that electromagnetic radiation have due nature. Wave nature as confirmed by experiments and particle nature is confirmed by photo electric effect.

de Broglie proposed that matter exhibits dual behaviour i.e. matter shows both particle and wave nature.

1. de Broglie’s relation: l = =

Where: l - Wavelength;  p – Momentum;   v – Velocity;  h – Planck’s constant

2. According to de Broglie, every object in motion has a wave character. Wavelengths of macroscopic objects cannot be detected but for microscopic particles it can be detected. This is because for microscopic objects, the mass is less. Since mass and wavelength are inversely proportional to each other, the wavelength will be more. But for macroscopic objects, the mass is large. Therefore, wavelength will be too short to be detected. Dual

Heisenberg’s uncertainty principle

It states that it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron

 

Assuming mass is constant and does not change with velocity

Schrodinger wave equation

The probability of finding an electron at a point within an atom is proportional to the  square of the orbital wave function i.e., ψ² at that point. ψ² is known as probability density and is always positive. From the value of ψ2 at different points within an atom, it is possible to predict the region around the nucleus where electron will most probably be found

IMPORTANT FEATURES OF THE QUANTUM MECHANICAL MODEL OF ATOM

Quantum mechanical model of atom is the picture of the structure of the atom, which emerges from the application of the Schrödinger equation to atoms. The following are the important features of the quantum me chemical model of atom:

1. The energy of electrons in atoms is quantized (i.e., can only have certain specific values), for example when electrons are bound to the nucleus in atoms.

2. The existence of quantized electronic energy levels is a direct result of the wave like properties of electrons and is allowed solutions of Schrödinger wave equation.

3. Both the exact position and exact velocity of an electron in an atom cannot be determined simultaneously (Heisenberg uncertainty principle). The path of an electron in an atom therefore, can never be determined or known accurately. That is why, as you shall see later on, one talks of only probability of finding the electron at different points in an atom.

4. An atomic orbital is the wave function ψ for an electron in an atom. Whenever an electron is described by a wave function, we say that the electron occupies that orbital. Since many such wave functions are possible for an electron, there are many atomic orbitals in an atom. These one electron orbital wave functions.  or orbitals form the basis of the electronic structure of atoms. In each orbital, the electron has a definite energy. An orbital cannot contain more than two electrons. In a multi-electron atom, the electrons are filled in various orbitals in the order of increasing energy. For each electron of a multi-electron atom, there shall, therefore, be an orbital wave function characteristic of the orbital it occupies. All the information about the electron in an atom is stored in its orbital wave function ψ and quantum mechanics makes it possible to extract this information out of ψ.

ORBITALS AND QUANTUM NUMBERS

ORBIT VS. ORBITAL

 PHYSICAL SIGNIFICANCE OF THE QUANTUM NUMBERS

1s and 2s orbitals

 2s and 2p Orbitals

d orbital

 ELECTRONIC CONFIGURATION OF ATOMS

Aufbau principle Electrons are placed in the lowest energetically available subshell. Thus orbitals are filled in the order of increasing energy, using two general rules  to help predict electronic configurations:-

1. Electrons are assigned to orbitals in order of increasing value of (n+ℓ). Orbitals with lower value of (n+l) are filled first as they have lower energy.
2. For subshells with the same value of (n+ℓ), electrons are assigned first to the sub shell with lower n.
3. The order in which the orbitals are filled is as follows:
4. 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 4f, 5d, 6p, 7s...
5. It is based on (n+ l) rule. It states that the orbital with lower value of (n +l) has lower energy.

 AUFBAU DIAGRAM

PAULI'S EXCLUSION PRINCIPLE

It is impossible for any two electrons of an atom to have the same values of the all four quantum numbers. If even three quantum numbers are same for any two electrons of the atom then fourth quantum number will definitely be different.

In other words an orbital can have maximum of two electrons

Hund’s Rule of Maximum Multiplicity

This rule deals filling of electrons in the orbitals belonging to the same subshells of equal energy called degenerate orbitals.

5.  It states that pairing of electrons in the orbitals belonging to the same sub shell (p, d or f) does not take place until each orbital of that sub shell gets one electron that is singly occupied.
5.  Some of the orbitals acquire extra stability due to their symmetry.

 EXCEPTION: HALF-FILLED AND FILLED D ORBITALS

•  When a subshell is half-filled or completely filled, it lowers the overall energy of the atom.
•  In other words, this is favoured.
•  This usually doesn't affect electron configurations, except in the d and f subshells.
•  Example: Copper (29 electrons)
•  Normal electron configuration:

      1s²2s²2p⁶3s²3p⁶4s²3d⁹

•  Added stability if 3 d is full (electron gets promoted to 3 d from 4s)
•  1s²2s²2p⁶3s²3p⁶4s¹3d¹⁰

The region where this probability density function reduces to zero is called nodal surfaces or simply nodes.

Boundary surface diagram: In this representation, a boundary surface or contour surface is drawn in space for an orbital on which the value of probability density ψ ²(r) is constant. However, for a given orbital, only that boundary surface diagram of constant probability density is taken to be good representation of the shape of the orbital which encloses a region or volume in which the probability of finding the electron is very high, say, 90%.

Radial nodes: Radial nodes occur when the probability density wave function for the electron is zero on a spherical surface of a particular radius. Number of radial nodes = n – l – 1

Angular nodes: Angular nodes occur when the probability density wave function for the electron is zero along the directions specified by a particular angle. Number of angular nodes = l

Total number of nodes = n – 1

Degenerate orbitals: Orbitals having the same energy are called degenerate orbitals

IMPORTANT FORMULAE

1.         
2. Frequency of electromagnetic wave  
3. Energy of photon E = hn =  
4. 
5. Bohr’s postulate mvr =  (Angular momentum of ‘e’ in an orbit)            
6. 
7. r_n = r₁ x n²  same atom different orbit
8. r_Z  = r_H / Z   same orbit different atom
9. 
10. u_n = u₁ / n        same atom different orbit
11. u_Z = u_H x Z      same orbit different atom
12.   E₁ for H= -21.72X10^-12 erg  = -13.6 eV
13. E_n = E₁/n²             same atom different orbit
14. E_Z = E_H x Z²    same orbit different atom
15. 
16. A^o
17. Ön=a (Z – b), where n is frequency of X-rays given out by metal of at. No. Z
18. Average atomic weight =  
19. KE of photoelectric electron (½ mv²) = hn - hn_o (hn_o = work function) & n_o threshold frequency
20. deBroglie equation l =  
21. Uncertainty
22. (Schrodinger wave equation)  
23. Angular momentum of ‘e’ in an orbital=  
24. Magnetic moment of an atom=.  where n is no. of unpaired electrons
25. Nodes
    1. Radial (spherical) nodes=(n – l – 1)
    2. Angular (non spherical) nodes=l
    3. Total nodes= (n - 1) 
26. No of spectral lines =