At what speed does the electron move around the nucleus?
VIJETH J. SHETTY, Udupi, Karnataka
The physics of subatomic particles like the electrons is governed by laws and rules of quantum mechanics rather than those of the classical physics applicable to relatively large or macroscopic bodies such as a cricket ball, a bus or a planet. However, the transition from the classical physics to the then new realm took place in a somewhat gradual manner.
Though today it is well established that the electrons do not have definite trajectories, in the beginning of the twentieth century, Prof. Neils Bohr made revolutionary postulates of definite stationary circular orbits for the electron in a hydrogen atom and demonstrated the success of this new approach though the theoretical derivation of the experimentally observed line spectrum of hydrogen atom. This gave the necessary credence to the model though its inadequacy was very soon discovered and rectified.
Within the Bohr's model, one can talk of electrons moving on a circular orbit where the centrifugal force it experiences by virtue of the circular motion is exactly balanced by the electrostatic attraction towards the centrally placed positively charged nucleus.
The radius of this circle in the hydrogen atom is called the Bohr radius and has a value of 0.529 angstrom units (1 angstrom = 10 {+-}{+1}{+0} m). The mass of an electron is 9.109 x 10 {+-}{+3}{+1} kg. The electric charge on the electron and the hydrogen nucleus (which is just a proton) is -/+ 1.602 x 10 {+-} {+1}{+9} Coulomb. Using these values along with the dielectric constant of free space to be 8.854 x 10 {+-} {+1}{+2} Farad per meter, it is possible to make an estimate of the speed of the electron in the circular orbit of the hydrogen atom to be about 2.188 x 10 {+6} meters per second or 2188 km/sec. This speed is about 150 times smaller than the speed of light in free space.
However, even within this early quantum description, the above estimate must be used with care because the circular orbit model does not hold good for all other atoms where the electron orbits are in general elliptical which take circular shape only in a limit.
And in an elliptic orbit, the centrifugal force keeps varying at every point, so does the distance of the electron from the nucleus whose charge is different from that of just one proton as we used for hydrogen nucleus. So, the electron speed at every point on the orbit can be different.
The more complete and modern quantum theory does not admit such definite and precise orbits but rather describes the existence of the electron through a probabilistic description.
Here, under any given circumstance, there is a probability of finding the electron at a point in space and at any instant of time. This keeps on changing from place to place and from time to time. In a sense, one can picturise the atomic electron to be a negative charge cloud around the nucleus, different electrons in any atom having different spatial shape of its charge distribution.
Therefore, in this picture we cannot talk of speed of an electron around the nucleus.
Prof. H. K. SAHU, Chennai Mathematical Institute, Chennai
