Structure of Atom 4 Flashcards
what is the dual nature of matter
einstein suggested that light has dual nature- both wave and particle nature
similarly de broglies suggested that all material particeles m like eelctron protion both microscopic and macroscopic have dual nature
the wave associated with a particle is called matter wave or de broglie wave.
how was de broglie’s proposal confirmed
de Broglie’s
prediction was confirmed experimentally
when it was found that an electron beam
undergoes diffraction, a phenomenon
characteristic of waves. This fact has been put
to use in making an electron microscope
when is de broglie wavelength significant
llion times.
It needs to be noted that according to de
Broglie, every object in motion has a wave
character. The wavelengths associated with
ordinary objects are so short (because of their
large masses) that their wave properties
cannot be detected. The wavelengths
associated with electrons and other subatomic
particles (with very small mass) can however
be detected experimentally.
what is it the heisenberg’s uncertainty principle ?
It states that it is impossible to simultaneously and acurately determine the exact position and exact momentum or velocity) of an electron.
Δx * Δp= h/4 ⊓
Δx * Δv = h/4m ⊓
what is the meaning of heinsenberg uncertainty principle
If the position of
the electron is known with high degree of
accuracy (∆x is small), then the velocity of the
electron will be uncertain [∆(vx
) is large]. On the other hand, if the velocity of the electron is
known precisely (∆(vx
) is small), then the
position of the electron will be uncertain
(∆x will be large). Thus, if we carry out some
physical measurements on the electron’s
position or velocity, the outcome will always
depict a fuzzy or blur picture.
what does heisenberg principle rule out
it
rules out existence of definite paths or
trajectories of electrons and other similar
particles. The trajectory of an object is
determined by its location and velocity at
various moments. If we know where a body is
at a particular instant and if we also know its
velocity and the forces acting on it at that
instant, we can tell where the body would be
sometime later. We, therefore, conclude that
the position of an object and its velocity fix
its trajectory. Since for a sub-atomic object
such as an electron, it is not possible simultaneously to determine the position and
velocity at any given instant to an arbitrary
degree of precision, it is not possible to talk
of the trajectory of an electron.
the heinsenberg uncertainty principle is only for microscopic particles explain
The effect of Heisenberg Uncertainty
Principle is significant only for motion of
microscopic objects and is negligible for
that of macroscopic objects.
If uncertainty principle is applied to an
object of mass, say about a milligram (10–6
kg), then
Δx . Δv = approx. 10 ⁻²⁸ m²s⁻¹
The value of ∆v∆x obtained is extremely
small and is insignificant. Therefore, one may
say that in dealing with milligram-sized or
heavier objects, the associated
uncertainties are hardly of any real
consequence.
explain with example tht heisenberg equation holds for microscopic things like electron
In the case of a microscopic object like an
electron on the other hand. ∆v.∆x obtained is
much larger and such uncertainties are of
real consequence. For example, for an electron
whose mass is 9.11×10–31 kg., according to
Heisenberg uncertainty principle
Δx . Δv = 10.⁻⁴m²s⁻¹
It, therefore, means that if one tries to find
the exact location of the electron, say to an uncertainty of only 10–8 m, then the
uncertainty ∆v in velocity would be
10⁴ms⁻¹
which is so large that the classical picture of
electrons moving in Bohr’s orbits (fixed)
cannot hold good.
what does heisenberg quantum mechanicla modle of atom do?
It, therefore, means that
the precise statements of the position and
momentum of electrons have to be
replaced by the statements of probability,
that the electron has at a given position
and momentum. This is what happens in
the quantum mechanical model of atom.
What is the schrodinger equation
For a system (such as an atom or a
molecule whose energy does not change with
time) the Schrödinger equation is written as
H ψ = Eψ where H is a mathematical
operator called Hamiltonian. Schrödinger
gave a recipe of constructing this operator
from the expression for the total energy of
the system. The total energy of the system
takes into account the kinetic energies of all
the sub-atomic particles (electrons, nuclei),
attractive potential between the electrons and
nuclei and repulsive potential among the
electrons and nuclei individually. Solution of
this equation gives E and ψ
postulates of quantum mechaical model
- The energy of electrons in atoms is
quantized (i.e., can only have certain
specific values) - It is based on Schrodinger Wave equation:
H ψ = Eψ
Where H-> Hamiltonian Operator
ψ-> Orbital wave function
The solution of the Schrodinger equation gives he values of E and ψ, where E gives all the possible energies values of the system. - In each orbital, the
electron has a definite energy. An orbital
cannot contain more than two electrons and must have opposite spin,
In a multi-electron atom, the electrons are
filled in various orbitals in the order of
increasing energy.
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.
- 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 of an electron is stored in the wave function psi of that electron.
6.. 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.
The probability of finding an electron at a
point within an atom is proportional to the
square of the orbital wave function i.e.,
|ψ|² at that point. |ψ|² is known as
probability density and is always
positive. From the value of |ψ|² at
different points within an atom, it is
possible to predict the region around
the nucleus where electron will most
probably be found.
what happens when schrodinger equation is solved ?
When Schrödinger equation is solved for
hydrogen atom, the solution gives the
possible energy levels the electron can occupy
and the corresponding wave function(s) (ψ)
of the electron associated with each energy
level. These quantized energy states and
corresponding wave functions which are
characterized by a set of three quantum
numbers (principal quantum number n,
azimuthal quantum number l and
magnetic quantum number ml ) arise as a
natural consequence in the solution of the
Schrödinger equation.
