Force, centripetal electrostatic

Bohr theory A theory introduced in 1911 to explain the spectrum of atomic hydrogen. The model he used was that of a nucleus with charge +e, orbited by an electron with charge -e, moving in a circle of radius r. If t> is the velocity of the electron, the centripetal force, mtP-lr is equal to the force of electrostatic attraction, e lAne r. Using this, it can be shown that the total energy of the electron (kinetic and potential) is -e /STKof. 

Let us illustrate the Heisenberg principle by considering motion of an electron in a hydrogen atom. The position of the electron and the momentum is assumed to be measured with an uncertainty equal to 0.01% - a commonly acceptable accuracy in engineering. The centripetal force equals to the force of electrostatic attraction between the electron and the nuclei. The velocity of the electron can be found from the equation... 

If the electron is to maintain a stable orbit, the electrostatic force and the centripetal force must be the same. Therefore, Eqs. 2.1 and 2.5 give... 

In a planetary system, the centripetal force is provided by the gravitational pull of the Sun. In atoms, this force comes from electrostatic interaction... 

If the electron is moving in a circular orbit of radius r then the electrostatic attraction force it experiences is balanced by the centripetal force ... 

In each stable orbit the electrostatic attraction between the negatively charged electron and the positively charged nucleus provides the centripetal force needed for the circular motion of the electron. The energy of the atom is the sum of the potential energy of electrostratic... 

Recently, a compact but powerful mass analyzer - the Orbitrap -was introduced (Fig. 2.12b) (39). Using a balance between the centripetal influence of an electrostatic field developed on a central electrode and the opposite centrifugal force of ions rapidly injected and moving in the mass analyzer, the Orbitrap produces packets of ions according to their m/z. The trajectory of ion motion inside the Orbitrap resembles a complex spiral orbit-... 

The centripetal force is provided by the electrostatic attraction of the positive nucleus for the negative electron. Coulomb s law for the force between a charge Q i and another charge Q2 separated by a vacuum is... 

A double-focusing mass spectrometer combines a magnetic sector such as the one described above with an electrostatic sector. The system is composed of two curved parallel electrodes (Figure 4.25) between which a difference of potential is applied in order for an electrostatic force of a value of E to exert itself perpendicularly to the surfaces of the electrodes. In absolute values, the intensity of this force is worth zE. For an ion to cross the electrostatic sector, this force must match its centripetal force mvVrE where r is the radius of the circular trajectory of the ion in the electrostatic sector. This condition utilizes the equality ... 

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