What is the approximate speed of an electron in a hydrogen atom's first orbit?

Around 2.2 × 10⁶ m/s—that’s about 1% the speed of light!

What happens if an electron in a hydrogen atom jumps to n = ∞?

The atom ionizes—the electron completely escapes, and the atom is no longer neutral!

Why don’t electrons exist between energy levels?

Energy levels are quantized, meaning electrons can only exist in fixed orbits where their wave fits perfectly.

The Balmer series appears in the visible spectrum. What’s the color of the longest wavelength transition?

Red—at 656 nm, when an electron falls from n = 3 to n = 2.

An alpha particle (charge = +2e) moves toward a gold nucleus (Z = 79) with 7.7 MeV energy. 
Find its closest approach distance using:

3.0 × 10^-14 m (or 30 fm)

Find the energy of an electron in the third orbit of hydrogen. Use:

An electron in hydrogen jumps from n = 4 to n = 2. The energy released is 2.55 eV. Find the emitted photon's frequency using:
E = hν, h = 6.63 × 10⁻³⁴Js, 1eV = 1.6 × 10⁻¹⁹J

Find the wavelength of the emitted photon for the n = 3 to n = 2 transition. Use:

The frequency of revolution of the electron in the nnnth orbit varies as

Number of possible spectral lines when an electron drops from n=5n=5n=5 to ground state (all paths allowed):

A) 4 
B) 5 
   C) 10 
D) 6

c) 10

Which observation in gold-foil experiment shows atoms are mostly empty space?

Most α-particles pass straight with little/no deflection.