![3. Since de Broglie believed particles and wave have the same traits,
he hypothesized that the two energies would be equal:
mc2=hν
4. Because real particles do not travel at the speed of light, De
Broglie submitted velocity (v) for the speed of light (c).
mv2=hν
5. Through the equation λ, de Broglie substituted v/λ for ν and
arrived at the final expression that relates wavelength and particle
with speed.
mv2=h v/λ
Hence:
λ=hv/mv2
=h/mv
=h/p
[p= momentum of particle=mv]](https://image.slidesharecdn.com/quantumno-231008125421-0169f67e/85/Quantum-no-ppt-9-320.jpg)
Quantum no.ppt
- 1. The Electron Cloud Model (wave-mechanical or quantum-mechanical model) • An atom consists of a dense nucleus composed of protons and neutrons surrounded by electrons that exist in different clouds at the various energy levels. REGION OF PROBABILITY • Erwin Schrodinger and Werner Heisenburg developed probability functions to determine the regions or clouds in which electrons would most likely be found.
- 2. The Heisenberg Uncertainty Principle Whenever a measurement is made there is always some uncertainty
- 3. The Heisenberg Uncertainty Principle The Heisenberg uncertainty principle states that it is impossible to know both the momentum and the position of a particle at the same time. This limitation is critical when dealing with small particles such as electrons. But it does not matter for ordinary-sized objects such as cars or airplanes.
- 4. The Heisenberg Uncertainty Principle To locate an electron, you might strike it with a photon. The electron has such a small mass that striking it with a photon affects its motion in a way that cannot be predicted accurately. The very act of measuring the position of the electron changes its momentum, making its momentum uncertain.
- 5. The Heisenberg Uncertainty Principle Before collision: A photon strikes an electron during an attempt to observe the electron’s position. After collision: The impact changes the electron’s momentum, making it uncertain.
- 6. The Heisenberg Uncertainty Principle If we want accuracy in position, we must use short wavelength photons because the best resolution we can get is about the wavelength of the radiation used. Short wavelength radiation implies high frequency, high energy photons. When these collide with the electrons, they transfer more momentum to the target. If we use longer wavelength, i.e less energetic photons, we compromise resolution and position.
- 7. The de Broglie wavelength is the wavelength, λ, associated with a object and is related to its momentum and mass. Introduction In 1923, Louis de Broglie, a French physicist, proposed a hypothesis to explain the theory of the atomic structure. By using a series of substitution de Broglie hypothesizes particles to hold properties of waves. Within a few years, de Broglie's hypothesis was tested by scientists shooting electrons and rays of lights through slits. What scientists discovered was the electron stream acted the same was as light proving de Broglie correct. De Broglie wavelength
- 8. Deriving the De Broglie Wavelength 1. De Broglie first used Einstein's famous equation relating matter and energy: E=mc2 with •E= energy, •m= mass, •c= speed of light 2. Using Planck's theory which states every quantum of a wave has a discrete amount of energy given by Planck's equation: E=hν with •E= energy, •h= Plank's constant (6.62607 x 10-34 J s), •ν= frequency
- 9. 3. Since de Broglie believed particles and wave have the same traits, he hypothesized that the two energies would be equal: mc2=hν 4. Because real particles do not travel at the speed of light, De Broglie submitted velocity (v) for the speed of light (c). mv2=hν 5. Through the equation λ, de Broglie substituted v/λ for ν and arrived at the final expression that relates wavelength and particle with speed. mv2=h v/λ Hence: λ=hv/mv2 =h/mv =h/p [p= momentum of particle=mv]
- 11. Ground versus Excited State • Electrons have the ability to move between energy levels. • The “ground state” refers the energy level that a given electron usually belongs to. • The “excited state” refers to a higher energy level that a given electron moves to as it gains energy. • Electrons that have gained energy and “jumped” to the excited state will eventually return to the ground state and release its energy in the form of a photon (light energy). • As a result of this process, different atoms will give off (emit) unique (characteristic) colors (bands) of light. This is called the Bright Line Spectrum.
- 13. What are Quantum Numbers? An electron’s unique “fingerprint” that describes it position and behavior
- 14. Quantum numbers are a set of values that describes the state of an electron including its distance from the nucleus, the orientation and type of orbital where it is likely to be found, and its spin.
- 15. Principal quantum number (n) - describes the SIZE of the orbital or ENERGY LEVEL of the atom. Angular quantum number (l) or sublevels - describes the SHAPE of the orbital. Quantum Numbers
- 16. Magnetic quantum number (m) - describes an orbital's ORIENTATION in space. Spin quantum number (s) - describes the SPIN or direction (clockwise or counter-clockwise) in which an electron spins. Quantum Numbers
- 17. Principle Quantum Number (n) or Energy Level integer values used to specify the shell/size/level the electron is in describes how far away from the nucleus the electron shell or level under consideration is the lower the number, the closer the energy level is to the atom's nucleus and less energy maximum # of electrons that can fit in an energy level is given by formula 2n2
- 18. The principal quantum number, n, describes the energy level on which the orbital resides. The values of n are integers ≥ 0. n = 1, 2, 3, etc.
- 20. Angular Quantum Number (l) or Sub-level determines the shape of the orbital they are numbered but are also given letters referring to the orbital type Allowed values of l are integers ranging from 0 to n − 1. For example, if n = 1, l = 0 if n = 2, l can equal 0 or 1
- 21. They are numbered but are also given letters referring to the orbital type l=0 refers to the s-orbitals l=1 refers to the p-orbitals l=2 refers to the d-orbitals l=3 refers to the f-orbitals
- 22. Magnetic quantum number (m) or Orbitals the third of a set of quantum numbers tells us how many orbitals there are of a particular type and their orientation in space of a particular orbital only two electrons can fit in an orbital = electron
- 23. Describes the orientation of an orbital with respect to a magnetic field This translates as the three-dimensional orientation of the orbital. Values of ml are integers ranging from -l to l: −l ≤ ml ≤ l. Values of l Values of ml Orbital designation Number of orbitals 0 0 s 1 1 -1, 0, +1 p 3 2 -2, -1, 0, +1, +2 d 5 3 -3, -2, -1, 0, +1, +2, +3 f 7
- 25. Spin quantum number (s) the fourth of a set of quantum numbers number specifying the direction of the spin of an electron around its own axis. only two electrons of opposite spin may occupy an orbit the only possible values of a spin quantum number are +1/2 or -1/2.
- 26. The aufbau principle: The aufbau principle states that in the ground state of an atom or ion, electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels.The aufbau principle is sometimes called the building-up principle or the Aufbau rule. For example, the 1s shell is filled before the 2s subshell is occupied. In this way, the electrons of an atom or ion form the most stable electron configuration possible. Hund's Rule: Every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin
- 28. Name Symbol Permitted Values Property principal n positive integers(1,2,3,…) Energy level angular momentum l integers from 0 to n-1 orbital shape (probability distribution) (The l values 0, 1, 2, and 3 correspond to s, p, d, and f orbitals, respectively.) magnetic ml integers from -l to 0 to +l orbital orientation spin ms +1/2 or -1/2 direction of e- spin Quantum Numbers of Electrons in Atoms
- 36. ORBIT ORBITAL It is well-defined circular path followed by electron around nucleus. It is a region of space around the nucleus where the probability of finding an electron is maximum. It represents two dimensional motion of electron around nucleus. It represents three dimensional motion of electron around nucleus. The maximum no. of electrons in an orbit is 2n2. The maximum no. of electrons in an orbital is 2. Orbit is circular in shape. Orbitals have different shapes. Orbits are non directional Orbitals are directional in nature except s orbital.