Structure of atom class 11 NEET/CBSE

J.J Thomson

discovered electron through cathode ray tubes.

• utilized Faraday’s study of electric discharge

• found e/me value

Cathode Rays

• move from (-) to (+) [cathode to anode]

• they are invisibe

  • used a perforated anode (had holes in the anode) and a Phosphorescent Zinc sulphide coating behind the anode - that helped see the cathode rays when they hit the coating)

• Travel in a straight line in the absence of a electric or magnetic field.

  • in the presence, cathode rays behave like (-) charged particles ——— electrons

• The characteristic of cathode rays do not depend on the nature of gas used or the material of the elctrodes (e/me ratio is constant)

why are electrons the basic constituents of all atoms

Electrons mass and charge do not change even if emitted from various sources and various methods (e/me ratio remains the same)

e/me ratio

(electron charge) x (electron mass) = 1.7 × 10¹¹

Millikan

through his oil drop experiment he found out electron charge.

electron charge value

-1.6 × 10^-19 C

proton charge

1.6 × 10^^-19 C

electron mass

9.1 × 10^-31 kg

proton mass

1.672 × 10^-27 Kg

neutron mass

1.674 × 10^-27 Kg

Goldstein

Discovered protons

• used a perforated cathode (cathode with holes in it)

  • anode rays emerge from the anode - a stream of (+) charged particles

Anode rays /canal rays

• A stream of (+) charged particles

  • consisted of POSITIVE IONS

  • in case of H, the anode rays consisted of protons

    • H ——> H⁺ + e^-

• They travel in a striaght line

• go from (+) to (-)

• The properties of anode rays depend on the nature of gas. (e/m ratio is different for different gases)

• The mass of positive particles is the same as the mass of the gas inside the tube

• The magnitude of the positive charge depends on the number of electrons lost

  • A - 2e^- ——→ A²⁺

  • A - 1e^- ———> A¹⁺

why do are the cathode ray tubes kept in very low pressure?

• there is enough space at low pressure

• allows gaseous atoms to accelerate at high speed

  • so when they strike each other they can eject electrons and create positive ions as well.

Chadwick

• discovered neutron

  • bombarded a thin sheath of Be with alpha particles which emmitted electrically neutral particles

difference between alpha particles and He

Alpha - has 2 protons and 2 neutrons

He - has 2 protons, 2 neutrons and 2 electrons

Thomson’s atomic model

Plum pudding model

• electrons are unevenly distributed in a sphere having positive charge

IMPORTANT FEATHURE - mass of atom is uniformly distributed over the whole atom.

FAILURE - due to Rutherford’s alpha scattering experiment

Rutherford

discovered nucleus

• narrow beam of alpha particles pass through a lead plate and falls on a thin gold foil which has a circular zinc sulphide screen surrounding it

Results of alpha scattering experiment

1. Most alpha particles passed through the foil with no deflection - most of the atom consists of empty space

2. Few alpha particles deflected at small angles - positive charge is concentrated at a very small space

3. Very few of them deflected completely (180). - The (+) charged core is called nucleus

   • volume occupied by the nuclues is very small (10^-10) with the radius of atom being 10^-15)

Rutherfords nuclear model of atom

• Nucleus - mass and (+) charge is centrally located in a small space

• protons + neutrons = nucleons

• the nucleus is surrounded by revolving electrons

• resembled the solar system

drawbacks of Rutherfords Model

1. Could not account for the stability of an atom

   • Due to Maxwells electromagnetic theory which states that a charged particle with acceleration emits radiation and looses energy

   • an electron will loose energy and crash into the nucleus (it will take it less than 10^-8 seconds )

2. Did not give any info about how electrons and distributed and the energy of these electrons

Atomic number (Z)

= number of protons = number of electrons in a neutral atom

Mass number (A)

Number of protons + number of neutrons

isotopes

same element, with different number of neutrons (different mass number)

Isobars

different elements with the same mass number

isotones

atoms with the same number of neutrons

isoelelectronic species

atoms that have the same number of electrons

Deuterium

an isotope of Hydrogen

has 1p 1e and 1n

developements leading to Bohrs model of atom

Dual character of electromagnetic radiation - both wave and particle like characters

Quantisation of energy

James Maxwell - wave nature of electromagnetic radiation

[Newton considered light as a stream of particles (corpuscles) but this concept could not explain the diffraction of light]

• Electromagnetic radiations have a electric and magnetic field which are perpendicular to each other as well as perpendicular to direction of the propagation of wave

• Do not need a medium to travel, can travel in vacuum . (speed = 3 × 10⁸ m/s)

electromagnetic spectrum

visible region - 400nm to 750nm

• consists of Violet, indigo, blue, green, yellow, orange, red

Cosmic rays < Gamma rays < X rays < Ultraviolet < visible light < Infrared < microwave < radiowaves

(in the order of increasing wavelength)

define wavelength

λ (lambda)

Wavelength is the distance between successive crests (or troughs) of a wave,

• inversely related to frequency; as wavelength increases, frequency decreases, and vice versa.

define frequency (ν)

Frequency is the # of waves passing though a paticular point in one second

Wave number (ṽ)

1/λ

• number of waves per meter

Amplitude

Height of crest or depth of trough

• determines intensity/brightness/loudness of the light

Velocity ( c )

The distance travelled in one second by the wave

• c=νλ

• where c = 3 × 10⁸

wave nature could explain

• diffraction (bending of wave around a obstacle)

• interference (combination of two waves to give a new wave)

wave nature could not explain

• Black body radiation (radiation from hot bodies + why they change colour)

• Photoelectric effect (ejection of electrons from a metal surface when striked with radiation)

• Line spectra of atoms w.r.t. H

• Variation of heat capacity of solids as a function of temperature

Plancks Quantum theory: particle nature of electromagnetic radiation

• black body radiation

• photoelectric effect

• atomic spectra

• line spectrum of hydrogen

black body radiation

• Black body is an ideal body that emits and absorbs radiations of all frequencies.

  • No such body exists in reality

  • carbon black is the closest thing to a black body

• the only factor on which the intensity and frequency of the emitted radiation depends is temp.

Max Planck

• atoms and molecules could emit or absorb energy only in discrete quantities and not in a continuous manner.

• Qauntum - smallest quantity of energy (it is called photon in case of light)

  • E=nhν

    • h = 6.626 × 10^-34 Js (Plancks constant)

    • n → number of quanta

  • if we put c=λν into the equation,

    • E=nhc/λ

Photoelectric effect

• electrons were ejected out of a metal surface when exposed to radiation

  • electrons were ejected out from the surface as soon as the beam of light hit - there is no time lag between the striking of light beam and the ejection of electrons

  • The number of electrons ejected ∝ intensity or brightness of light

    • DOES NOT DEPEND ON FREQUENCY

  • For each metal there is a threshold frequency - Min. amount of Energy required to eject electron from metal to overcome binding energy

    • binding energy=threshold energy

incident energy (E_i)

energy we put on an experiment

photoelectric equation

E_i = E_o + KE

• E_o - threshold energy

  • can also be replaced by BE (binding energy)

  • BE=hν_o=Work function

• KE - kinetic energy of the electron when ejected out.

  • depends on the frequency of light

• Only if E_i > E_o photoelectric effect occurs

hν_i = hν_o + ½ m_ev²

Evidence for the quantized electronic energy levels : atomic spectra

emission and absorption spectrum (line spectrums or discrete spectrums)

• electron will always try to remain in the lowest energy level

experiment -

1. heat a gas

2. electron will jump to a higher energy level (energy absorbed) - absorption spectrum

3. electron will go back to its original energy level (energy released) - emission spectrum

continuous spectrum

VIBGYOR

• has all the colours

spectroscopy

study of line spectrums

line spectrum

• every element has its own unique line spectrum

• fingerprints of atoms

line spectrum of hydrogen (will complete later)

Bohrs model of hydrogen and hydrogen like atoms

Postulates :

1. The electron moves around the nucleus in circular paths of fixed radius and energy

   • called orbits/stationary states/energy states

2. Energy of an electron does not change with time but

   • electron can move from n₁ to n₂ while absorbing energy

   • electron can move from n2 to n1 while releasing energy

3. Bohrs frequency rule

   • frequency of energy released from the transitions from 2. ^

     • ν = ΔE / h

       • ν = (E2-E1) / h

4. The angular momentum (L) of electron is quantised.

   • mvr=n x h/2π

     • m → mass of electron

     • v → velocity of electron

     • h → 6.626 × 10^-34

     • n = 1,2,3,...

Meaning of n

n is just the numbering for the orbits/stationary states/ energy levels for electron

so the first energy state will be n=1

2nd energy state n=2 and so on

Radii of stationary states

r_n= a_o (n²/Z ) pm

a_o = 52.9 pm → Bohr orbit, the radii of the first energy state for H

Z = atomic number for hydrogen like atoms

energy of stationary states

E_n= -R_H (Z²/n²)

• -R_H → Rydbergs constant = -2.18 × 10^-18 J = -13.6 eV/atom

  • energy for the ground state for H (n=1) is -R_H

Why the negative sign in E_n= - R_H (Z²/n²) ?

An electron's energy under an atom's influence is lower than the energy of an electron that is not under the influence of an atom (E=0). SO when the electron gets closer to the nucleus, its Energy gets lower (more negative)

• a free electron’s energy is depicted as E=0

• the energy of an electron at n=1 will be the lowest (most negative)

velocity of electron

V∝Z (positive charge on nucleus)

V∝ 1/n (principle quantum number)

V = 2.18 × 10⁶Z / n m/s

energy gap between 2 orbits

ΔE=E_f - E_i

hc/λ = -R_H(Z²/n_f²) - - R_H (Z²/n_i²)

hc/λ = R_HZ² ( 1/n_i² - 1/n_f² )

Limitations of Bohr’s Model

1. Could not explain line spectra of multielectron systems

2. Could not explain ability of atoms to form molecules by chemical bonds

3. Failed to explain splitting of spectral line under the presence of a magnetic field (Zeeman effect) or an electric field (Stark effect)

4. could not account for the finer details in Hydrogen spectral lines. (Using sophisticated spectroscopic techniques it was observed that the spectral lines had doublets or triplets → closely spaces lines)

developments leading towards quantum mechanical model of atom

1. Dual behavior of matter

2. Heisenberg’s Uncertainty Principle

de-Broglie - dual behavior of matter

Just like radiation, matter should exhibit both particle and wave-like properties (dual behavior)

λ=h/p

• derived from E=hν and E=mc²

  • hν=mc²

• not significant for macroscopic objects

Heisenberg uncertainty principle

It is impossible to determine the exact position and the exact momentum of an electron simultaneously

Δx ⋅ Δp ≥ h/4π

• Δx → error in position

• Δp → error in momentum

Significance

• rules out the existence of definite paths or trajectories of electrons and other similar particles

• only significant for microscopic objects

quantum mechanical model

Based on quantum mechanics

• developed by Heisenberg and Schrodinger

  • Schrodinger wave equation

    

Ψ (Psi)

• does not carry any physical meaning

  • 3D wave function

| Ψ | ²

probability density of finding electron at that point within an atom

maximum probability region is actually what is atomic orbital

What are the three quantum numbers that are solutions of the Schrödinger wave equation?

• Principle quantum number (n)

• Azimuthal quantum number (l)

• Magnetic orbital quantum number (m_l)

Which quantum number is not a solution to the Schrodinger wave equation?

electron spin quantum number (m_s)

Principal quantum number (n)

• represent which shell the electron is in

  • n=1,2,3,…

• Determines the energy and size of an orbit

• number of electron in a shell = 2n²

• number of orbitals in a shell = n²

Azimuthal Quantum number (l)

also known as subsidiary quantum number

• gives us ORBITAL angular momentum (in Bohrs postulates it was ORBIT angular momentum)

  • h/2π √l(l + 1)

• gives 3D shape of the orbital

• number of orbitals in a subshell = 2l + 1

• number of subshells in a shell = n

• 0 → s

• 1 → p

• 2 → d

• 3 → f

Magnetic orbital quantum number (m_l)

• gives us total number of orbitals in a given subshell (l)

• spatial orientation of the orbital w.r.t standard set of co-ordinate axis

• explains Zeeman effect

fyi

orbit or shell → n

subshell → l

orbital → m_l

electron spin quantum number (m_s)

Tells us wether the electron is spinning clockwise or anticlockwise, explained the presence of two closely spaces lines in spectral lines (doublets)

• +1/2 → clockwise

• -1/2 → anticlockwise

an orbital cannot have more than two electrons and those two electrons must have opposite spins

nodes

where probability of finding an electrons is 0

total nodes = n - l

Radial nodes

= n-1-l

angular nodes

= l

shapes of atomic orbitals

s → spherical

p → dumb bell shaped

d → double dumbbell

d_z² and d_x²-y² (degenerate d orbitals)

degenerate

orbitals having the same energy

energy of orbitals

the orbital with the lower (n+l) value has lower energy

• if they have the same n+l value then the orbital having lower value of n has lower energy

Aufbau Principle

electron filling takes place in order of increasing energy of subshells (from lower energy subshell → higher energy subshell)

note : when removing electrons from an atom, you remove it from the outermost subshell and you do not follow aufbau principle!

• ex - 4s and 3d even tho 3d has higher energy and you would fill up 4s first, when removing electron you would remove from 4s and not 3d

Hund’s rule of maximum multiplicity

an electron will fill each orbital first before pairing together

• because half filled (or) fully filled orbitals are highly stable

Pauli’s exclusion principle

no 2 electrons in an atom will have the same set of all 4 quantum numbers

electronic configuration of Chromium (Cr) - 24

[Ar]4s¹, 3d⁵

• this occurs because half filled oribitals are more stable

Cu - 29 E.C

[Ar] 4s¹, 3d¹⁰