I have read the quantum mechanical model of an atom which says that path of an electron around the nucleus is uncertain due to uncertainity principle which says that it is impossible to measure both momentum and position of an electron at the same time so it is impossible for an electron to move in a well defined circular orbit.But what if we simply do not measure the elcetron then it should move in a well defined path.So what really restrict it from moving like that?
They do not follow Newtonian physics since they exhibit distinctively wave properties,objects of large size dont show wave properties distinctively and hence wave like properties are negligible.They do not revolve around nucleus as defined by Bohr,here the wave properties of the particles comes into play. According to Bohr,electrons exhibit particle like properties and revolve around nucleus in well defined orbits but it failed experimentally as Heisenberg couldn't simultaneously determine the position and the velocity of the electron.
German physicist Warner Heisenberg had proposed that the position and the velocity of an object cannot both be measured exactly, at the same time, even in theory. The very concepts of exact position and exact velocity together, in fact, have no meaning in nature.
Ordinary experience provides no clue of this principle. It is easy to measure both the position and the velocity of, say, an automobile, because the uncertainties implied by this principle for ordinary objects are too small to be observed. The complete rule stipulates that the product of the uncertainties in position and velocity is equal to or greater than a tiny physical quantity, or constant (h/(4π), where h is Planck’s constant, or about 6.6 × 10−34 joule-second). Only for the exceedingly small masses of atoms and subatomic particles does the product of the uncertainties become significant.
Any attempt to measure precisely the velocity of a subatomic particle, such as an electron, will knock it about in an unpredictable way, so that a simultaneous measurement of its position has no validity. This result has nothing to do with inadequacies in the measuring instruments, the technique, or the observer; it arises out of the intimate connection in nature between particles and waves in the realm of subatomic dimensions.
Every particle has a wave associated with it; each particle actually exhibits wavelike behaviour. The particle is most likely to be found in those places where the undulations of the wave are greatest, or most intense. The more intense the undulations of the associated wave become, however, the more ill defined becomes the wavelength, which in turn determines the momentum of the particle. So a strictly localized wave has an indeterminate wavelength; its associated particle, while having a definite position, has no certain velocity. A particle wave having a well-defined wavelength, on the other hand, is spread out; the associated particle, while having a rather precise velocity, may be almost anywhere. A quite accurate measurement of one observable involves a relatively large uncertainty in the measurement of the other.
The uncertainty principle is alternatively expressed in terms of a particle’s momentum and position. The momentum of a particle is equal to the product of its mass times its velocity. Thus, the product of the uncertainties in the momentum and the position of a particle equals h/(4π) or more. The principle applies to other related (conjugate) pairs of observables, such as energy and time: the product of the uncertainty in an energy measurement and the uncertainty in the time interval during which the measurement is made also equals h/(4π) or more. The same relation holds, for an unstable atom or nucleus, between the uncertainty in the quantity of energy radiated and the uncertainty in the lifetime of the unstable system as it makes a transition to a more stable state.
This of course follows from the uncertainty principle, but more generally, there is an important concept in quantum mechanics known as the principle of complementarity. Essentially this boils down to the fact that physical systems have certain properties that cannot be observed simultaneously, most notably, the particle and wave duality of electrons.
Regarding your question, the idea that the electron follows a well defined trajectory when we do not measure is is completely untrue, as if the particle had a well defined trajectory then it would also have a well defined position and momentum at all times, violating the uncertainty principle. Because of this uncertainty, it only makes sense to talk about the position and momentum as probability distributions.
The particle/wave duality provides a way to visualize this using systems we are used to in the classical world. If an electron had a well defined trajectory, it would mean that the electron is a particle, but it also acts as a wave. Suppose I throw a rock into a pond of water, and wait for a second as the water waves spread out radially. At this point I ask you, where is the water wave? Well, it's in many places at once, but it's not a kilometre away, as it's still localized to the region close to where I threw the rock. Similarly, there is a notion of having an electron localized in some region around the atom, without having a well defined position.