why angular momentum of electron in atom is different one electron to another for same energy state?

Question

Electron of specific energy state in atom is having different angular momentum to each other to fulfil exclussion principle and depicts the shape of the orbit. But if angular momentum differs how about the energy of state. If "l" value is 0 is that means angular momentum is zero. please answer.

Answer 1

Here we need to clarify the concept of angular momentum as it applies to sub-atomic particles. The key concept is called "spin", which refers to the angular momentum "intrinsic" to a body, as opposed to orbital angular momentum, which is the motion of a body's center of mass about an external point.

In classical mechanics, the angular momentum of a body is associated with the rotation of the body around its own center of mass. In quantum mechanics, spin is particularly important for systems at atomic length scales, such as individual atoms, protons, or electrons. Such particles and the spin of quantum mechanical systems ("particle spin") possesses several unusual or non-classical features, and for such systems, spin angular momentum CANNOT be associated with rotation but instead refers only to the presence of angular momentum, which is a truly intrinsic physical property, like electric charge and mass.

In atoms, the atomic orbitals are the quantum states that electrons surrounding an atom may exist in. These quantum states can be described by 3 sets of orbital quantum numbers: n, l, and m, where n is the principal quantum number which determines the size and energy of the orbitals, l is azimuthal quantum number which determines an orbital's shape, and m is the magnetic quantum number which determines its orientation. So here "l" is NOT equal to the "angular momentum" or "spin" of the atomic orbitals.

So to answer your question, yes, it is possible for 2 electrons to occupy the same energy states, beause they have different spin. For electrons, it's spin can be ±1/2.

Answer 2

An electrons angular momentum is equal to:
L = (h/2*pi)sqrt(l(l+1))

plugging 0 into the formula does produce 0. So, yes, l=0 means 0 angular momentum.

remember that an electron still has non-zero intrinsic spin, so when you put it into a magnetic field that changes intensity in some direction then the electron will act as if it is spinning.

Also, these quantum variables fall out of the partial differnential wave equation (shrodigners (sp)). What you do to solve it is you need to make a subsitution that allows you to seperate the equation into three seperate ordinary differential equations. These can then be solved for different values of l,m, and n.

Answer 3

Agular momentum is another indicator describing that a moving mass has rotational energy.
The Energy cannot be a state because it does not exist statically.

The Energy levels in the Bohr's atom and the differences were just a model to fit the Empirical formulas that His predecessors had formulated concerning the radiation spectrum .
The formula of angular momentum left out mass changes with velocity. That is why his model did not work for the more complexs atoms.

So what was really meant by energy level was really the structured mass energy content at that particular orbit.So that the electron mass did change with velocity . This is what Einstein alluded in his mass change formula. It basically applied to the mass changes in the electron.

Answer 4

The L states have slightly different energies where as teh Lz states are projections of the z-component of the angular momentum of the L state. Lz measures the direction of the rotational angular momentum. For L = 1, Lz can project along the z- axis (Lz=1), antiparallel to it (Lz=-1) or perpendicular to it (Lz = 0) the only way to observe this is to place the atom in a magneitc field that forces the states to align along a preferred direction. Then you get splitting of transisitons due to conservation of angular momentum and angular momentum in each spatial direction. L = 0 only has one projection state Lz=0. It is degenreate int hat it can have two electrons with same L, Lz but different spins.

Answer 5

orbit is a space where electon and not a specific path which electron follows dude there fore electrons found in this space are found at different places hence have different momentum

Answer 6

See "Uncertainty Principle" by Werner Heisenberg