Where the negative sign is telling us that we have to do work on the electron to increase its radius, or to put it another way that the force acts towards the centre but the radius vector acts away from the centre of the electron’s orbit. Where is an incremental change in the radius. So we can derive the potential energy of an electron in orbit due to the Coulomb force as Energy is the capacity to do work, and is measured in the same units, Joules. What about the potential energy? The potential energy can be found by using the relationship between work and force back in this blog I said that work was defined as the force multiplied by the distance moved. The total energy of the electron in its orbit is given by the sum of its kinetic energy and its potential energy. This is, indeed, about the size of a hydrogen atom. The so-called “Bohr radius” is the radius of an electron in the energy level for hydrogen ( ) and can be written Where is the energy level of the electron. This allows us to write an expression for the “radius” of an electron’s orbit as Which then allows us to write the angular momentum as

Where is the mass of the electron and is the speed of its orbit. We can equate this to the formula for the centripetal force on any object moving in a circular orbit, so we can write The minus sign is telling us that the force is directed towards the centre, whereas our definition of the radius vector is that it is away from the centre, so they are in opposite directions.

Where is the Coulomb constant (which determines the force between two 1 Coulomb charges separated by 1 metre), is the atomic number of the atom, is the charge on an electron and is the radius of the orbit. The force keeping the electron in orbitįrom Classical Physics, Bohr argued that the force which was keeping the electron in orbit about the positively charged nucleus was the well known Coulomb force, given by For a circular orbit, where the radius vector is at right angles to the velocity vector, we can just write where is the magnitude (size) of the vector. Where is the radius vector of the orbit, which is defined as pointing from the centre of the orbit along the radius. Notice, momentum is a vector quantity, this is important in doing calculations involving collisions, such as the ones I did in this blog.īy analogy, orbital angular momenutm is defined as What is orbital angular momentum? Well, it is the rotational equivalent of linear momentum. ( is Planck’s constant, and is given its own symbol in Physics at it crops up so often). He suggested that these allowed orbits were when the orbital angular momentum could be written as If they were in these special orbits, the normal laws of EM radiation would not apply. They clearly were not doing this, but why?īohr suggested in a paper in 1913 that electrons would somehow not radiate away their energy if they were orbiting in certain “allowed orbits”. Calculations showed that the orbiting electrons on Rutherford’s model should radiate away their energy in a few microseconds (millionths of a second), and spiral towards the nucleus. It was well known that when an electron is accelerated it radiates electromagnetic waves. The acceleration is directed towards the centre of the circle. One of the problems with this idea was that an orbiting electron would be accelerating, by virtue of moving in a circle. In 1911, Rutherford had proposed that atoms have positively charged nuclei, with the negatively charged electrons orbiting the nuclei.

In this blog I will go into more detail about this model, and how it agreed with the experimental results (the Rydberg formula) for the hydrogen atom. In my blog on Niels Bohr, number 2 in The Guardian’s list of the 10 best physicists, I mentioned the Bohr model of the atom.

Bohr model of the atom definition