What determine's the shape of an orbital?

Question

An orbital has many shapes like spherical,dumbbell etc.But,on what basis is the shape determined?

Answer 1

i had this same question once! Well, the shape of different orbitals can be explained by schrodinger's equation which is :
d^2psi/dx^2 + d^2psi/dy^2 + d^2psi/dz^2 + 8(pi)^2m/h^2(E-V)psi=0
u see it works like this, the curvature of the wave function of the electron (psi) varies with K.E. of the particle. higher the k.e. greater will be the curvature and hence shorter will be the wavelength. the curvature of psi is given by second order differential of psi with respect to x,y and z for three dimensional representation of psi. this concept gave birth to the above equation.here E is the total energy and V is the potential energy.
the solution of the above equation is possible for some discrete values of E indicating different energy states E1, E2, E3, which also depends on the structure of the atom.
the quantum nos, ie, n,l,m all came as solutions of the above equation. hence the above equation is extremely important. but its use is limited to atoms of one-electron system only ie, (H-atom like).
If you know high advanced maths u can deduce the geometric shapes of different orbitals yourself.But the solutions are very complicated. You can try the various university-level physics books if you want a complete answer.

Answer 2

The orbit an object goes into when it gets captured depends on its entry vector. That vector includes direction and velocity components, and totally determines the orbit the object will acheive, both initially, and finally.

For example, our moon is moving away from earth, so it's orbit is not stable, and we shall lose the moon. In reality, no orbit is ever stable because any movement within a either a magnetic or gravittional field generates tidal forces that continually alter the orbit of the orbiting body. Those tiday forces are slowing down the antular rotation of the earth, and speeding up the orbital velocity of the moon (because the earth spins faster than the moon orbits), so the moon is climbing into ever-higher orbits.

But, if you look at it short-term, it depends on the velocity, and angle of entry into the capturing bodies gravitational field... (That is described by a vector.)

Ron.

Answer 3

An orbital what? If you mean the electron's orbit around the nucleus, quantum physics requires that the length of the orbit be an integral multiple of the wavelength of the electron's wavefunction. For a hydrogen atom, it's elliptical, nearly circular. For more complex atoms, each individual orbit of an electron is affected by interaction with other electrons in the same shell and those in neighboring shells. Quantum limits on observability prevent us from accurately measuring a particular orbit.

It's worse in a molecule, whose covalent bonds involve some outer shell electrons orbiting more than one nucleus. That's where the bond derives its strength, because the total energy of such a molecule is lower than the isolated component atoms.

Answer 4

When the potential is apherically symmertric, the schrodinger equation is separable into an angular and a radial equation. The solutions to the angular equation are the spherical harmonics.