Does energy change with change in position of electron (in quantum model)? In the quantum model of atom, an electron has a probability of being found anywhere in the space (except nodes). Now suppose a first shell electron ($n=1$) is present at a distance $r1$ from the nucleus and has energy $E$. Now if the next instant it is present at a new distance $r2$ from nucleus, will the energy change or remain the same? If no, then why? If yes, then how can we say that principal quantum number determines the energy of the electron? What would be the physical meaning of shell then?
 A: Here are the hydrogen wave function solutions in space, for (r,θ,φ)

and further in the link.
The energy of the electron is basically  given by the level of the n quantum number (with some corrections for the spin state), In the simple Bohr model the values are given here, which do not differ from the correct quantum mechanical solution. So the electron in its orbital ( not orbit) has a probability given by $Ψ^*Ψ$ to be at a particular (r,θ,φ) if measured.

Now suppose a first shell electron (n=1) is present at a distance 'r1' from the nucleus and has energy E. Now if the next instant it is present at a new distance 'r2' from nucleus, will the energy change or remain the same?

The wavefunction gives only the possibility of calculating probabilities, it is not tied like a quantum number on the electron, that is the misunderstanding. It does not describe where the electron is in space, but just the probability of finding the electron at (r,θ,φ) if measured at an arbitrary time. The energy is always the one characterized by the n quamtum number. It does not change.
To get an idea, look how the orbitals available for electrons in the hydrogen solution look.

A: "a first shell electron (n=1) is present at a distance $r_1$ from the nucleus and has energy $E$."
Quantum-mechanically this is impossible. The Hamilton-operator does not commute with  the position operator. So having an electron at energy $E$ and at a known position $r_1$ is impossible.
So of course you could measure the position. But if you do so, the electron will be in a pure position state. However, then the information on the energy state is completely lost. The position state can be decomposed in a series of energy states, and nobody would know in which of these energy states the electron would be. So you can measure the energy state again, but in the very same moment you loose the information of the electron's position ...
This said, it is impossible to know position and energy of an electron at the same time and all speculations about this are make no sense in Quantum mechanics.
A: In a classical framework, the total energy of the electron is its potential energy plus its kinetic energy (although to be precise, the electric potential energy is a property of the entire system, not just the electron). So in the classical model, an electron that's close to the nucleus would have higher velocity than one farther from the nucleus. This only partly translates to the quantum picture, but there is some correspondence for the correctly formulated quantities.
A: The way I see it you have the other way around, which is the source of your confusion.
From a quantum mechanical standpoint the possible energies are the eigenvalues of the Hamiltonian. There really is no other way to look at it. The Hamiltonian is dependent on space is the potential and possibly via interactions.
Thus energies are a functional of space dependent functions, but not coordinate dependent explicitly.
That being said, the converse is true. I.e. the probability of measuring a particle at a certain position depends on is energy.
From a probability point of view the energy and position of a particle are two dependent random variables, drawn from separate distributions.
