explain why electrons cannot orbit the nucleus of an atom at random energies?

Answer 1

Because at each enrgy level the deBroglie equivalent wave has to contain an integral number of cycles (that is, there are no 'fractional' deBroglie equivalents).

Doug

Answer 2

The energy of an electron is determined by it's orbital shell. The higher the orbit, the higher the energy. This allows the atom to either absorb or radiate energy. Absorbing energy causes electrons to move to higher orbits, and releasing energy the opposite. The number of positions per shell (places than can hold an electron) is represented by the number of columns per row in the periodic table.

Answer 3

If they could then there would be no characteristic spectral lines in the light emitted by atoms. Also, any accelerating charge, such as an orbiting electron, would radiate away all its energy in a fraction of a second and fall into the nucleus.

Answer 4

Doug is absolutely right and he should get the ten points. Electrons in an atom are not really particles in the strictest sense. They are best descibed as wave functions, and standing waves to be precise. Standing waves must have a whole number of wavelengths in order to be stable. I suppose a fractional wholenumber standing wave could exist for maybe a femtosecond, but it would very quickly settle down into a whole number arrangement or else fly away from the atom completely. I hope this helps.

Answer 5

Nature loves balance and stability, as in music. Keep it simple. Random means chaos, and you know what dear professor Einstein said: God does not play dice with the universe. Thank you.

Answer 6

the atom would be unstable, electrons would fly off.