Question

What do scientists use to predict the location of electrons in atoms?

Answer 1

As we know atoms are considered to be the smallest entity in any matter, detailed study of this tiniest particle is quite difficult. So studying and predicting the location of the particle which is inside the atom is very difficult. This particle is an electron. Electrons have a mass of $9.109 \times {10^{ - 31}}kg$ this is so negligible that it is not even included in the atomic mass of an atom.

Complete answer:
As the uncertainty principle states “It is impossible to precisely measure the momentum and position of the particle with great accuracy “.
If we measure the momentum with exactness its position preciseness will change automatically.
So, the method which scientists use to predict is “THE PROBABILITY” of finding the particle.
Schrodinger gave this theory for the study of particles quantum theory.
In which he treated the electron as in three dimensional manner and as
Schrodinger equation:
$\dfrac{{{\partial ^2}\Psi }}{{\partial {x^2}}} + \dfrac{{{\partial ^2}\Psi }}{{\partial {y^2}}} + \dfrac{{{\partial ^2}\Psi }}{{\partial {z^2}}} + \dfrac{{8{\pi ^2}m}}{{{h^2}}} + (E - V)\Psi = 0$
Where x, y, z are space coordinates, m=mass of electron, h=Planck’s constant, E=total energy, V=potential energy.

Note:
Physical significance of $\Psi$ represents the amplitude of the electron wave.
${\Psi ^2}$ at a point is proportional to probability of finding the particle, the probability is more near the nucleus and the point where probability is more is called electron density.