Structure of Atoms Class 11 Notes

Structure of Atoms

  MCQs  

Particles	Electron	Proton	Neutrons
Discovery	J.J.Thomson	Goldstein	Chadwick
Year	1869	1886	1932
Nature of Charge	Negative	Positive	Neutral
Amount of Charge	1.6 X 10−19C	1.6 X 10−19C	0
Mass	9.11 X 10−31kg	1.67 X 10−27kg	1.67 X 10−27kg

Discovery of Electron

J.J.Thomson experiment
Discovery of electron is the result of the study of electric discharge in the discharge tube.
Discharge tube consists of a glass tube with two metal electrode called cathode and anode fused in the wall. With the help of vaccum pump, air is evacuated from the tube. A high potential of 10,000 volt is connected to the electrodes under very low pressure 10^{−2 to −4} atm. The electric discharge passes between the electrodes and the residual gasses in the tube being to glow green. If virtually all the gasses is evacuated within the tube, the glow is faintly replaced by faintly luminous rays which produce fluorescence on the glass at the far end from the cathode. The ray which produce at cathode and moves in straight way with very high velocity to anode are called Cathode Rays as it produced from cathode.

Properties of Cathode Rays

Followings are the important properties of the Cathode Rays-
1. They travel in staright line away from cathode with very high velocity ranging from 10⁷ to 10⁹ m/sec.
2. They produce a caste shadow on the opposite to the cathode when a metallic object is placed in their path.
3. They produce green glow when strick the glass wall and light is emitted when they strick the ZnS screen.
4. When a small pin wheel is placed in their path, the blade of the wheel comes to in motion that means cathode rays consists of material particles which ghas mass and velocity.
5. They produce heat energy when they collide with matter that means cathode rays has kinetic energy.
6. They are deflected by electrical and magnetic field.
7. These rays affect the photographic plate like light.
8. Cathode rays can ionize the gasses through which they passes.
9. The nature of cathode rays is independent of-
a. nature of cathode materials &
b. gasses in discharge tube.
10. Cathode rays is negatively charged as it produced from −ve electrode.
In 1891, Johnstone Stoney propsed the name electrom when J.JThomson discovered the light particles which carried tahat charge.

Discovery of Proton

In 1886, Goldstein used a discharge tube with a perforated cathode. He observed that while cathode rays were streaming away from the cathode, there were colored rays produced simultaneously which passed through the perforated cathode and caused a glow on the wall opposite to the anode.
Thomson studies these rays and shows that they consists of particles carrying a +ve charge. He called them positive rays.
Explanation
When high speed cathode rays(i.e electrons) strick gas molecules placed in the discharge tube, they knock out one or more electrons from it. Thus a +ve ion results.
M → M⁺ + e⁻
These positive ions passed through the perforated cathode and appears as a +ve rays.
Goldstein discovered proton in the discharge tube contining hydrogen.
H → H⁺ + e⁻
Anode rays(i.e positive rays) is generated from gas between the cathode and anode and not from the material of anode.

Properties of Positive Rays

Followings are the main properties of positive rays:-
1. They travel in a straight line in a direction opposite to the cathode.
2. They are deflected by electric as well as magnetic field in such a way that they are +vely charged.
3. They possess mass many times the mass of an electron.
4. The charge to mass ratio (e/m) of positive particles varies with nature of the gas placed in the discharge tube. The hydrogen gas gives the highest value for e/m. The e/m ratio for hydrogen was found 1.67x 10^-24g and taken as standard.
5. They cause fluorescence in ZnS.

Discovery of Neutron

Neutron was discovered by Chadwick in 1932 by the bumbardment of α particle on berylium atom.
₄B⁹ + ₂α⁴ → ₆C¹² + ₀n¹
Neutron is chargless. So, there is no effect of electric and magnetic field. Its mass is almost equal to that of proton. It is found in all atoms except protium. Its half life period is 20 minutes only. It generates rotons by self decomposition.
n → e + p + Q
Its position in atom is nucleus.

Determination of the Charge on an electron

The absolute value of charge on an electron was measured by R.A.Millikan in 1908 by what is known as the Millikan's oil drop experiment.
The apparatus used by him is shown in figure.
He sprayed oil droplets from an atomizer into the apperatus. An oil droplets falls through a hole in the upper plate. The air in the upper plates is then expressed to x-rays which eject electron from air molecules. Some of these electrons are captured by the oil droplets and it aquire a negative charge. When the plates are earthed, the droplets falls under the influence of gravity. After his experiment Millikan found that the charge on the electron is −1.6 X 10⁻¹⁹C.

Determination of the Mass of an electron

Mass of the electron was determined by the combination of Thomson's 'e/m' value and Millikan's 'e' value.
Mass of electron (M_e) = e/(e/m)
or, M_e = (1.6 X 10⁻¹⁹C) / (1.76 X 10⁸g/m)
or, M_e = 9.1 X 10⁻²⁸gm

Atomic Number (Z)

Number of protons present in an atom is known as its atomic number.
In a neutral atom, Atomic number = Number of protons (np) = Number of electrons present. It is represented by the letter 'Z'.

Mass Number (A)

The mass of an atom is mainly due to protons and neutrons. These two subatomic particles are collectively known as nucleons. The total number of protons and neutrons in the nucleus is called mass number of the atom. It is generally represented by the letter 'A'.
Mass number = No. of protons + Number of Neutron

Isotopes

Atoms of an element with the same atomic number but different mass numbers are called isotopes. For example, hydrogen has three isotopes. They are Protium (¹H), Deuterium (²H) and Tritium (³H). Carbon has three isotopes namely, ¹²C, ¹³C, ¹⁴C.

Isobars

Atoms having the same mass number but different atomic numbers are called Isobars. Examples:¹⁴C₆ and ¹⁴N₇, ⁴⁰Ar₁₈ and ⁴⁰K₁₉

Isotones

Atoms having the same number of neutrons but different mass numbers are called isotones. Examples: ³⁰Si₁₄, ³¹P₁₅, ³²S₁₆.

Wavelength (λ)

Distance between two consecutive crests or troughs is known as wavelength and is expressed in centimetres (cm), nanometres (nm) or angstrom (Å)
1nm = 1O^-9m = 10^-7cm
1 Å = 10^-10m = 10^-8cm

Frequency (ν)

It is the number of waves passing through a given point in one second and is expressed as cycles per second or hertz (Hz).
1 Hz = 1 cps.
Frequency is inversely proportional to wavelength of the wave
i.e. 𝜈 ∝ 1 / λ
or c = λ
where c is velocity of the wave.

Velocity (c)

It is defined as the distance travelled by a wave in one second.
Electromagnetic radiations travel with velocity of light (i.e. c = 3 x 10⁸ m/s).

Wave Number (𝑣̅)

It is the number of waves present in one cm length. It is reciprocal of wavelength.
i.e. 𝑣̅ = 1 / λ

Amplitude (a)

It is defined as the height of crest or depth of trough. It gives the intensity or brightness of the beam of light.

Electromagnetic Radiations or Electromagnetic Waves

Scottish physicist James Clark Maxwell in 1856 suggested that electromagnetic waves are produced by the motion of electrically charged particles. As they radiate from the electrically charged particles so, these waves are also called electromagnetic radiation. They travel through empty space as well as through air and other substances with the same velocity of light.
It has been observed that electromagnetic radiation has a dual nature. It behaves like waves as well as like a stream of particles (photons) that have no mass. The photons with the highest energy have shortest wavelengths.
The energy of electromagnetic radiation is directly proportional to its frequency or inversely proportional to its wavelength.

Electromagnetic Spectrum

The arrangement of different types of electromagnetic radiations in order of the increasing wavelength or decreasing frequency is known as electromagnetic spectrum.
The different regions of the electromagnetic spectrum are- Cosmic rays, γ-rays, x-rays, UV region, Visible region, Infrared region, Microwaves, Radiowaves etc.
Cosmic rays has highest energy and frequency while radiowaves has highest wavelength.
E = hν = h. c/λ
so, energy and frequency are directely related to each other and inversely related to wavelength.
Image Source: NASA Science

Q. Which of the following has the highest energy ?
a. X-rays
b. Ultraviolet radiation
c. Gamma rays
d. Infrared radiation

Electromagnetic Radiations and their Wavelengths

Radiations	Wavelength (Ao)
Radio waves	3×1014 to 3 ×107
Microwave	3×109 to 3 ×106
Infrared (IR)	6×106 to 7600
Visible	7600 to 3800
Ultra violet (UV)	3800 to 150
X-Rays	150 to 0.1
Gamma Rays	0.1 to 0.01

Black Body Radiation

When a body is heated, it emits electromagnetic radiation and when temperature is dropped, the energy is absorbed by the body. If a body absorbs all radiations that falls upon it, it is called the Black Body and the radiation emitted by it is called Black Body Radiation
No any object is perfectly black body.
In 1854, Kirchoff proposed the following two laws concerning black body. They are-
1. A black body not only absorbs all radiation falls upon it but also acts as a perfect radiator when heated.
2. The radiation given out by a black body depends upon the temperature of body and is not dependent on the nature of the interior materials.

Plank's Quantum Theory

This theory explains the spectral distribution of black body radiation. i.e. how the energy distributed among different wavelengths emitted by a black body.
Followings are the main points of this theory-
1. Energy emitted or absorbed is not continuous, but is in the form of packets called quanta. Quanta may be taken as behaving like a strem of particles having mass, energy and momentum. The energy of quantum radiation is-
E = h ν (where 'h' is Plank's Constant & 'ν' is frequency of radiation)
or, E ∝ ν
2. Each photon carries an energy in discrete level which is directly proportional to the frequency of wavelength. The energy of the nth enenrgy level is given as-
E = nhν
where 'n' is integer having values 0,1,2,3...

Compton Effect

When x-rays fall on a crystal, they are scatterd. Compton in 1923, observed that the wave length of the scattered radiation(λ^') is always greater that the wavelength of the incident radiation(λ)
i.e. λ^' > λ
The change in wavelength is independent of the wavelength of the incident radiation as well as that of scatterer. The change in wavelength of the scattered radiation is called Compton effect.

de-Broglie Wave Equation

The de Broglie equation is used to describe the wave properties of matter, specifically, the wave nature of the electron.
de Broglie equation states that a matter can act as waves and particles like light and radiation.
We know that Einstein's equation-
E = mc²     ---------(eq.1)
where, E = energy, m = mass the particles and c is the velocity of light
According to Plank's rdiation theory-
E = hν = h.c/λ     ---------(eq.2)
where, h = Plank's constant and λ = wave length of radiation
From equation 1 and 2 we have-
mc² = h.c/λ
or, mc = h/λ
or, p = h/λ     [as mass(m) X velocity(c) = momentum(p)]
or,   λ = h/p      ---------(eq.3)
Equation '3' is called de-Broglie Wave Equation.

Question: Find the de Broglie wavelength for an electron moving at the speed of 5.0×10⁶m/s (mass of an electron is 9.1×10⁻³¹kg )
[Hints: λ = h/mv
h = 6.63×10⁻³⁴J⋅s]
Answer: 1.46×10⁻¹⁰m

Heisenberg Uncertainty Principle

It is not possible to determine precisely and simultaneously the momentum and position of small moving particles.
If position of the particle is known then momentum is unknown and vice-versa.
Δx. Δp ≥ ℏ/2 = h/4π
where, Δx = uncertain position, Δp = uncertain momentum, ℏ = h/2π & h = Plank's constant
Δx. mΔv ≥ ℏ/2
Δx. Δv ≥ ℏ/2m
Δx. Δv ≥ h/4πm

Question: A particle is moving with constant momentum. The uncertainty in the momentum of the particle is 3.3 x 10^-2 kg ms^-1. Calculate the uncertainty position.
[Hints: Δx = ℏ/2.Δp
Δx = 5.27 ☓ 10^-35/3.3 ☓ 10^-2
1.59 ☓ 10^-33m]

Photoelectric Effect

When a beam of light of sufficiently high frequency is allowed to strike a light metal (IA) surface, electrons are ejected from the metal surface. This phenomenon is called photoelectric Effect.
Observations
An increase in the intensity of the incident light does not increase the energy of the photoelectrons. It mearly increases their rate of emission.
The kinetic energy of photoelectrons increases with the frequency of the incident light. If the frequency is decreased below a certain value (I.e. threshold frequency ν_o) no electrons are ejected at all.
Explanation
A photon of incident light transmits it's energy (hν) to an electron in the metal surface which escapes with kinetic energy 1/2mv². The greater intensity of incident light merely implies greater number of photons each of which releases one electron. This increases the rate of emission of electrons while the kinetic energy of individual photons remains unaffected.
The energy of a photon(hν) is proportional to the frequency of the incident light. The frequency which provides enough energy just to release the electron from the metal surface, will be threshold frequency v_o. For frequency less than ν_o , no electrons will be ejected or emitted.
For higher frequency, ν > ν_o,
hv = hv_o + 1/2 mv² ------(equation 1)
hv is energy of incoming photons
hv_o is minimum energy of an electron to escape from the metal.
1/2 mv² is kinetic energy of photoelectron
hv_o is constant for a particular solid and is denoted by letter w.
So, the work function -
1/2 mv² = hν - w ------ (equation 2)

Solar Spectrum

When sun light or any white light is passed through a prism, it dispersed i.e. separated into different colors. This assemblage of color is called a Spectrum. Different colors have different wave length as well as frequency. Seven types of colors obtained from a white light or sun light. They are Red, Orange, Yellow, Green, Blue, Indigo and Violet. These colors are falls in the wavelength region of 3800A° to 7600A°.
Red color has highest wavelength and lowest energy and lowest frequency so, less deviates while Violet color has lowest wavelength and highest frequency so it deviates more.

Hydrogen Spectrum

When an electric discharge is applied on gaseous hydrogen atom at low pressure, a bluish light is emitted. When a ray of this bluish light is passed through a prism, a spectrum of several isolated sharp line is obtained. The wavelength of various lines shows that the spectrum lines lie in the visible, ultraviolet and infrared region. These lines are grouped in different series. These series of lines are named after the scientists who discovered them. The limiting line (i.e. last line) of any spectral series in the hydrogen spectrum is the line when n₂ in the Rydberg's formula is infinity, i.e. n₂ = ∞. The wavelength of all these series can be expressed by a single formula which was given by Rydberg.

Series	Discovered by	Region	n2→n1	Number of Lines
Lyman	Lyman	U.V. Region	n2=2,3,4... & n1=1	n2−1
Balmer	Balmer	Visible Region	n2=3,4,5... & n1=2	n2−2
Paschen	Paschen	IR Region	n2=4,5,6... & n1=3	n2−3
Brackett	Brackett	IR Region	n2=5,6,7... & n1=4	n2−4
Pfund	Pfund	IR Region	n2=6,7,8... & n1=5	n2−5
Humphery	Humphery	Far IR Region	n2=7,8,9... & n1=6	n2−6

Rydberg Formula

Rydberg gave a theoretical equation for the calculation of wavelength of various lines of hydrogenic spectrum in 1890.

Where, R is Rydberg Constant and its value is equal to 109678cm⁻¹.
Derivation

Quantum Number

An atom contains number of orbits and orbitals. These are distinguished from one another on the basis of their size, shape and orientation in space. The parameters are given in terms of different numbers called quantum numbers. Quantum numbers may be defined as a set of four numbers with the help of which we can get complete information about all the electrons in an atom. Quantum number tells us the complete address of the electron (i.e. location, energy, the type of orbital occupied and orientation of that orbital) in an atom.

Quantum Number is of four types-
1. Principal Quantum Number (n)
2. Azimuthal Quantum Number (l)
3. Magnetic Quantum Number (m)
4. Spin Quantum Number (s)

Principal Quantum Number (n)

It is denoted by 'n'.
The values of 'n' can never be zero but from 1 to n.
n = 1 K shell
n = 2 L shell
n = 3 M shell
n = 4 N shell
'n' represents the orbit number (i.e. size of the atom) as well as energy of the orbit to which an electron belongs.
n ∝ R & E
As the value of 'n' increases, the energy of the electron increases and thus, the electron is less tightly held with nucleus. Angular momentum can be calculated using principal quantum number: mvr = nh/2π

Azimuthal Quantum Number (l)

i. It is denoted by 'l'and is represent the sub-shell (i.e. orbital)
ii. The value of 'l' depeds upon the value of 'n'.
iii. The values of 'l' are from 0 to (n − 1)
l = 0 for s-sub-shell, l = 1 for p-sub-shell, l = 2 for d-sub-shell and l = 3 for f-sub-shell
iv. For a given value of n, total values of 'l' are 'n'.
v. The values of 'l' signify the shape and energy level of sub-shells in a major energy shell.
vi. The number of electrons in a particular sub-shell is equal to 2(2l + 1)
vii. If the value of 'n' is same then the order of energy of various sub-shells of a shell will be s < p < d < f
4s < 4p < 4d < 4f
viii. If the value of 'l' is same but the value of 'n' is different then the order of energy of various sub-shells of a shell will be 1s < 2s < 3s < 4s < 5s < 6s
3d < 4d < 5d < 6d etc.
ix. The orbital angula momentum = √l(l+1)ℏ

Magnetic Quantum Number (m)

i. It is denoted by 'm'.
ii. It represents the orientation of orbitals.
iii. Its value depends upon the value of 'l'
m = − l to + l
iv. The positive values of magnetic quantum number 'm' represent the angular momentum component of the orbital in the direction of the applied magnetic field whereas the negative values of 'm' account for the angular momentum component of orbital in the opposite direction of applied magnetic field. v. Total values of 'm' for a given value of 'n' = n²
vi. Total values of 'm' for a given value of 'l' = (2l + 1)

Spin Quantum Number

i. It is denoted by 's'.
ii. It describe the orientation of the electron spin (rotation) in the space.
iii. The value of 'm' are +1/2(clockwise rotation) and −1/2(anticlockwise rotation)
iv. Magnitude of spin quantum number of an electron cannot be changed.
v. The spin may lie in 2s+1 = 2 orientation.
vi. Each type of subatomic particle has fixed spin quantum numbers like 0, 1/2, 1, 3/2, … etc.
vii. The spin value of an electron, proton and neutron is 1/2.
viii. The particles having half integral value (1/2, 3/2 …) of spin are called fermions.
ix. The particles having integral value (0, 1, 2..) of spin are called bosons.
x. Spin multiplicity of an atom is √s(s+1)
xi. Spin angular momentum of an electron is √s(s+1)h/2π

Question: Which of the following set of quantum number is not possible-
a. n = 2, l = 0, m = −1, s = −1/2
b. n = 3, l = 2, m = −1, s = +;1/2
c. n = 2, l = 1, m = −1, s = −1/2
d. n = 2, l = 3, m = −1, s = +;1/2

Question: What is the maximum number of electrons, which can have following quantum numbers
n = 3, l = 1, m = -1 ?
a. 2
b. 6
c. 8
d. 4

Pauli's Exclusion Principle

No two electrons in an atom can have the same set of all the numbers.
Example-
Quantum numbers of 5th and 6th electrons of nitrogen-
5th electron-
n = 2
l = 1
m = +1
s = +1/2

6th electron-
n = 2
l = 1
m = 0
s = +1/2
we have all the same quantum numbers except 'm' for 5th and 6th electrons of nitrogen.

Angular Node/Nodal Plane

The probability of finding an electron in nucleus is zero and is called a nodal point. Any plane passing through that point where the probability of finding an electron is zero is called a nodal plane.
s-orbital doesn't have any nodal plane.

p-orbital has one nodal plane.
Nodal plane-
for px is YZ plane
for py is XZ plane
for pz is XY plane.

d orbital has two nodal planes.
Nodal planes-
for dxy are XZ and YZ for dxz are YZ and XY
for dyz are XY and XZ
for dx²−y² are the lines inclined at 45° with X and Y axes.

Number of radial nodes = (n − l − 1)
Number of angular nodes = l
Total number of nodes = (n − 1)
Number of nodal planes = l

Applications of Bohr's Model

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