The electron doesn't fall into the nucleus b/c it can absorb and release energy. I'd suggest reviewing the Bohr Model of the atom and why Neils Bohr related the bright line emission spectrum of Hydrogen to electrons orbiting at 'discrete' distances from the nucleus. Basically, electrons absorb energy, jump outward from a low energy orbit to a higher energy orbit and then falls back to lower energy levels. During the 'electron transition' from a higher energy orbit to a lower energy orbit, light energy (photons) are emitted. If they stop at the n = 2 energy ( or, L-shell of the atom ) they will emit visible radiation which can be viewed using a diffraction grating or prism. Hydrogen gives 4 visible spectra lines, each having a 'discrete' wavelength. This means that the electron during energy level transitions will reside at a specific distance (discrete average, i.e., principle quantum number (n) according to Quantum Mechanics) from the nucleus. The electron starts its transition in a higher energy orbital, then it is in a lower energy orbital. It doesn't stop in between, or give evidence that it passed through the 'in between'. Such is called 'quantization,' or more commonly referred to as a 'quantum leap'. If they resided anywhere within the atomic volume, examination of the EMR Spectrum would be a Continuous Spectrum like the rainbow. Colors of the rain bow: ROY G BIV. From low energy to high energy ... Red, Orange, Yellow, Green, Blue, Indigo & Violet.
P.S. 'Infinite Energy' is the 1st (and only) Ionization Energy of the Hydrogen Atom. ∆Ei-1 = 2,8 x 10-18 Joule[ (1/n2)i - (1/n2)∞ ] = 2.8 x 10-18 Joule[ (1/n2)i ] where (1/∞2) = 0. Then ionization from the ground state configuration, n = 1 => ∆Ei-1 = 2.8 x 10-18 Joule/H-atom = [(2.18x10-18 x 6.02x1023) / 1000]Kj/mole = 1312 Kj/mole.