Sub-atomic Particles
Electron
Experiment used to discover electrons→Cathode Ray Tube Experiments
Experiment used to calculate Charge-to-Mass ratio→Cathode Ray Deflection
Experiment
Cathode Ray Tube Experiments results
Source and destination
Explanation→Cathode rays start from the cathode and move to the
anode.
Visibility of the rays
Explanation→The rays are invisible, but their behavior can be
observed with fluorescent or phosphorescent materials which glow when hit by the
rays.
Behavior in absence of fields
Explanation→In the absence of an electrical or magnetic field, the
rays travel in straight lines.
Behavior in presence of fields
Explanation→In the presence of an electrical or magnetic field, the
behavior of the cathode rays is similar to that of negatively charged particles,
suggesting that cathode rays consist of negatively charged particles called
electrons.
Characteristics' dependencies
Explanation→The characteristics of cathode rays (electrons) do not
depend upon the material of electrodes and the nature of gas present within the
cathode ray tube. So we can conclude that electrons are the basic constituent of
all atoms.
Cathode Ray Deflection Experiment
Performed by→J.J. Thomson
Results
Factors affecting deviation of particles from their path
The magnitude of the negative charge on the particle
Explanation→The greater the charge, the greater the
interaction with the electrical or magnetic field, so greater the deflection.
The mass of the particle
Explanation→The lighter the particle, the greater the
deflection.
The strength of the electrical or magnetic field
Explanation→The more the voltage across the electrodes or
strength of the magnetic field, the greater the deflection.
\frac{e}{m_e}
Value→1.759 x 1011 \frac{C}{kg}
Oil Drop Experiment
Performed by→R.A. Millikan
Description→Tiny oil droplets were atomized and allowed to enter a
chamber. The downward motion of the droplets could be viewed through a telescope.
The chamber contained two plates of an electric condenser. The air inside the
chamber was ionized with X-rays. The fall of the droplets could be retarded,
accelerated or made stationary depending on the charge on the droplets or the
voltage across the condenser.
Conclusions
The magnitude of electrical charge q on the droplets is always an
integral multiple of the fundamental value of electrical charge
Charge of electron
Charge→-1.6 x 10-19 C
m_e→ \frac{e}{m_e}= 9.11×10^{-31} kg
Protons and Neutrons
Canal rays
Characteristics
Dependencies
Explanation→The mass of positively charged particles
depends on the nature of gas present in the cathode ray tube.
Charge to mass ratio dependencies
Explanation→It depends on the gases from which they
originate.
Electric charge
Explanation→Some positively charged particles contain a
multiple of the fundamental unit of electric charge.
Behavior in magnetic and electric fields
Explanation→It is opposite to cathode rays.
Smallest and lightest positive ion→The proton (hydrogen ion)
Neutrons
Discoverer→James Chadwick
Prior Atomic Models
Elements
Thomson's Model of the Atom
Rutherford's Nuclear Model of the Atom
Bohr's Model of the Hydrogen Atom
Thomson's Model of the Atom
Features
The atom is a uniformly positively charged sphere.
Electrons are embedded in it in such a manner as to provide the most
stable electrostatic arrangement.
The mass of the atom is uniformly distributed throughout the atom.
Rutherford's Nuclear Model of the Atom
Radius of atom→10-10 m
Radius of nucleus→10-15 m
Alpha (\alpha)-particle Scattering Experiment
Setup→A stream of high energy alpha particles from a radioactive source
was directed at a thin foil of gold metal. The thin foil had a circular fluorescent
zinc sulphide screen around it. Whenever alpha-particles struct the screen, a tiny
flash was produced at that point.
Observations
Most \alpha-particles passed through the gold foil undetected.
A small fraction of the \alpha-particles was deflected by small
angles.
Very few particles (around 1 in 20,000) were deflected back by
almost 180°.
Conclusions
Most of the space in the atom is empty if most alpha particles
passed through undetected.
A positive charge has to concentrated in a very small volume in
order to repel and deflect some of the positively charged alpha particles.
The volume of the nucleus is negligibly small as compared to the
total volume of the atom.
Features
The positive charge and most of the mass of an atom is densely
concentrated in a very small region, called the nucleus.
The nucleus is surrounded by electrons that move around with a very
high speed in circular paths called orbits. This resembles a solar system.
Electrons and the nucleus are held together by electrostatic forces of
attraction.
Why can't the electrons in the model be considered stationary around the
nucleus?→Because then the electrostatic attraction between the nucleus and
electrons would pull the electrons towards the nucleus to form a miniature version
of Thomson's model of the atom.
Drawbacks
Stability of an atom
An electron orbiting the nucleus should undergo acceleration even
if it is moving at a constant speed because it is always changing direction.
According to the electromagnetic theory of Maxwell, charged particles emit
electromagnetic radiation under acceleration. This means the electron should lose
energy and spiral into the nucleus. But this does not happen, and so the model
cannot explain the stability of an atom.
Distribution of electrons
Rutherford's model says nothing about the distribution of the
electrons around the nucleus and the energies of these electrons.
Atomic Number and Mass Number
Atomic Number→(Z) Number of protons in the nucleus
Nucleons↔Protons and neutrons present in the nucleus collectively
Mass number→Number of nucleons, i.e., Z + number of neutrons (n)
Isobars and Isotopes
Isobars→Atoms with the same mass number but different atomic numbers.
Example→_6^{14}C and _{7}^{14}N
Isotopes→Atoms with the same atomic numbers but different mass number.
Examples
Hydrogen
Protium (_1^1H), Deuterium (_1^2D) and Tritium (_1^3T)
Carbon
_6^{12}C, _6^{13}C, _6^{14}C
Why do all isotopes of a given element show the same chemical behavior?
→Because the chemical properties of atoms are controlled by the number of
electrons, which is controlled by the number of protons. Neutrons have very little
effect on the chemical properties of an element, and they are the only differences
between isotopes.
Developments Leading to Bohr's Model
What were they?
Dual character of electromagnetic radiation, meaning that radiations
possess both particle- and wave-like properties.
Experimental results regarding atomic spectra
Electromagnetic Waves / Radiation→When an electrically charged particle moves
under acceleration, alternating electrical and magnetic fields are produced. These
fields are transmitted in the form of waves called electromagnetic waves.
Wave Nature of Electromagnetic Radiation
Behavioral properties
The direction of propagation of the wave, the oscillating magnetic
field and electric field are all perpendicular to each other.
Electromagnetic waves do not need a medium to travel, unlike sound
waves.
There are many different types of electromagnetic radiations, which
differ in frequency. They constitute the electromagnetic spectrum.
Different kinds of units are used to represent electromagnetic
radiation.
Properties
Frequency (\nu)
Definition→The number of waves passing through a given point per
second
SI unit and person it was named after→Hertz, Heinrich Hertz
Wavelength (\lambda)
SI unit→Meter (m)
Wavenumber (\tilde{\nu})
Definition→The number of wavelengths per unit length (1/\lambda)
SI unit→1/M (M-1)
Equation for speed of light→c = \nu\lambda
Black body→An ideal body which emits and absorbs radiations of all
frequencies uniformly
Black body radiation→Energy radiated by a black body that is determined
solely by its temperature
Quantum→The smallest quantity of energy that can be emitted or absorbed in
the form of electromagnetic radiation
Energy of a quantum (formula)→E = hv, where v is the frequency and h is
Planck's constant
Planck's Constant (h)→6.626 x 10-34 J s
Photoelectric Effect→When certain materials are exposed to a beam of light,
electrons are ejected
Results of experiment
Latency between striking and ejection
Explanation→Electrons are ejected as soon as the beam of light
strikes the surface. There is no time lag.
Number of electrons ejected
Explanation→The number of electrons ejected is directly
proportional to the intensity or brightness of the light.
Minimum frequency
Explanation→There is a minimum frequency below which electrons
will not be ejected.
Kinetic energy
Explanation→The kinetic energy of the ejected electrons is
directly proportional to the frequency of the light.
Kinetic energy of a electron→hv = hv_0 + \frac{1}{2}m_ev^2, where v is
the frequency of light, v_0 is the minimum frequency of the material, and v is the
velocity of the electron
Frequency of violet and red→7.50 x 1014 Hz, 4x1014 Hz, respectively
Atomic Spectra
Emission Spectrum↔The spectrum of radiation emitted by a substance that
has absorbed energy
Absorption Spectrum↔The spectrum of radiation with dark spaces
representing the wavelengths absorbed by a substance
Atomic Spectra // Line Spectra↔The emission spectra of atoms in the
gaseous state
Difference from other spectra→They emit light only at specific
wavelengths with dark spaces between them, rather than continuously like the
continuous visible spectrum. They are discrete, not continuous.
Significance→They can be used to identify unknown atoms, since each
element has a unique line emission spectrum.
Atomic spectra of gaseous atoms―They do not show a continuous
spread but rather dark spaces between specific wavelengths, since atoms emit light
only at specific wavelengths
Spectroscopy↔Study of emission or absorption spectra
Where was it used in the past?→Helium was discovered in the sun
using spectroscopy.
Line Spectrum of Hydrogen
Rydberg's expression→\bar{v} = 109677 (\frac{1}{n^2_1}-\frac{1}
{n^2_2}) cm^-1 , n_1 = 1, 2, 3..., n_2 = n_1 + 1, n_1 + 2...
Rydberg constant for hydrogen→109677 cm-1
Bohr's Model of the Hydrogen Atom
Postulates
Orbits
Orbit→A path around the nucleus with fixed radius and energy, also
called stationary state or allowed energy state.
Explanation→The electron in the hydrogen atom can move around the
nucleus in an orbit. Orbits are arranged concentrically around the nucleus.
Energy change
Explanation→The energy of an electron will not change, but if energy is
absorbed by the atom, the electron will move to a higher orbit. If an electron
moves to a lower orbit, energy will be released. The energy change is not
continuous.
Bohr's Frequency Rule
Rule→n = \frac{\Delta E}{h} = \frac{E_2 - E_1}{h}, where n is the
frequency of radiation absorbed or emitted, \Delta E is the difference in energies
between the states.
Explanation→The frequency of radiation absorbed or emitted when
transition occurs between two orbits that differ in energy by \Delta E is given by
Bohr's Frequency Rule.
Angular momentum of an electron
Angular momentum→Product of moment of inertia (I) and angular
velocity \omega. I is m_er^2 and \omega is \frac{v}{r} where v is the initial
velocity. So the final expression is m_evr
Explanation→The angular momentum of an electron is quantized. It is
described by: m_evr = n.\frac{h}{2\pi}, where n = 1, 2,3...
Energy of an electron
Formula→E_n = -R_H(\frac{Z^2}{n^2}) J, where R_H is the Rydberg Constant
Rydberg Constant→R_H = 2.18x10-18 J
Radius of a stationary state
Formula→r_n = \frac{52.9(n^2)}{Z} pm
Bohr orbit→First stationary state
Why does acceleration of an electron not cause it to radiate energy in Bohr's
model?→Because in Bohr's model, angular momentum is quantised, so energy is only
radiated when there is a transition from a higher stationary state to a lower
stationary state.
Limitations
It could not explain a doublet, or two closely spaced lines, observed in
the hydrogen atom.
It could not explain the line spectra of atoms other than hydrogen
It could not explain the splitting of spectral lines in the presence of a
magnetic field (Zeeman effect) or in an electric field (Stark effect).
It could not explain the ability of atoms to form molecules by chemical
bonds.
Towards the Quantum Mechanical Model of the Atom
Factors contributing to formation of Quantum Mechanical Model
Dual behaviour of matter
Heisenberg Uncertainty Principle https://remnote-user-
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Dual Behaviour of Matter
Person who proposed it→Louis de Broglie
de Broglie Equation→\lambda = \frac{h}{mv}
Heisenberg's Uncertainty Principle↔It is impossible to determine simultaneously
the exact position and exact momentum (or velocity) of an electron
Mathematical expression→\Delta x\times \Delta p_x \geq \frac{h}{4\pi} ,
or \Delta x\times \Delta v_x \geq \frac{h}{4\pi m} where \Delta x and \Delta p_x
are the uncertainties in position and momentum respectively
