Why do heavier atoms experience relavistic effects(contraction)?

[Redbelly98]

In hydrogen, n=1 .. Could -13.6 eV just be considered the force (or energy) holding the electron in place?

Well, it's the total energy, kinetic + potential. From the virial theorem (as atyy mentioned), this means that

U = -27.2 eV
and
K = +13.6 eV

The force "holding the electron" is due to the potential, -27.2 eV. But it's a little more complicated, since potential varies with distance from the nucleus and the electron's wavefunction is spread around in space. So these numbers for U and K represent averages. You could also think of them as the values for a circular Bohr-model orbit.

 

[Chaste]

Actually, I'm trying to explain quantatively why heavier atoms like gold have to be explained using relativistic contraction.

I fabricated my explanation but there's this contradicting part which I need help on.

From the probability density function of the atomic orbitals, it can be seen that electrons in higher n quantum number orbitals have certain probability to be close to the nucleus, which is what I learned as the penetrating power of higher n quantum number orbitals and is it because of this penetration that the electrons in higher n quantum number are drawn close to the nucleus and that's why experience its strong nuclear attraction? and thus increases its Kinetic energy to compensate to the strong coulombic forces. With increase in K.E, it translates to an increase in mass since E=mc². Following with an increase in mass of the electron, radius of the orbital the electron is in has to decrease as L=mvr=n(h/2pi) as L(angular momentum) has to be conserved and to be always an integer of (h/2pi).
Thus, that orbital contracts and brought further in proximity to the nucleus which results in stablizing of the orbital and thus, creating an inertness of that electron(s) in that orbital to partake in any bonding due to a great energy barrier.

Contradicting part is, I seemed to mention the orbital is drawn close to the nucleus TWICE.(bolded)

uhm, nobody has really commented if I sounded contradicting or not.

 

[Chaste]

Here's a cheating way to think about it. The sun is pulling us towards it. The reason we don't fall into the sun is we have a tangential velocity, so we fall round the sun, rather than into the sun. The closer you are to the sun, the greater the pull of gravity, and the greater your tangential velocity has to be to orbit the sun instead of falling into it. Similarly electrons that are closer to the nucleus go around faster.

I have a query... so if for example a 2p orbital, its orbital angular momentum always have to be conserved right? like M_l always have to be 1 or -1.
It cannot because of any factors change to become other integers right?