6.4 Bohr’s Model of the Hydrogen Atom

What are the limits of the Lyman series? Can you see these spectral lines?

When an electron in a hydrogen atom is in the first excited state, what prediction does the Bohr model give about its orbital speed and kinetic energy? What is the magnitude of its orbital angular momentum?

Do the various spectral lines of the hydrogen atom overlap?

When the absorption spectrum of hydrogen at room temperature is analyzed, absorption lines for the Lyman series are found, but none are found for the Balmer series. What does this tell us about the energy state of most hydrogen atoms at room temperature?

Discuss the similarities and differences between Thomson’s model of the hydrogen atom and Bohr’s model of the hydrogen atom.

If, in a hydrogen atom, an electron moves to an orbit with a larger radius, does the energy of the hydrogen atom increase or decrease?

Suppose an electron in a hydrogen atom makes a transition from the (n+1)th orbit to the nth orbit. Is the wavelength of the emitted photon longer for larger values of n, or for smaller values of n?

Can a hydrogen atom absorb a photon whose energy is greater than 13.6 eV?

Do gravitational forces have a significant effect on atomic energy levels?

Calculate the wavelength of the first line in the Lyman series and show that this line lies in the ultraviolet part of the spectrum.

Calculate the energy changes corresponding to the transitions of the hydrogen atom: (a) from $n = 3$ to $n = 4 ;$ (b) from $n = 2$ to $n = 1 ;$ and (c) from $n = 3$ to $n = \infty .$

What is the frequency of the photon absorbed when the hydrogen atom makes the transition from the ground state to the $n = 4$ state?

When a hydrogen atom is in its third excided state, what are the shortest and longest wavelengths of the photons it can emit?

For an electron in a hydrogen atom in the $n = 2$ state, compute: (a) the angular momentum; (b) the kinetic energy; (c) the potential energy; and (d) the total energy.

It has been measured that it required 0.850 eV to remove an electron from the hydrogen atom. In what state was the atom before the ionization happened?

Find the shortest wavelength in the Balmer series. In what part of the spectrum does this line lie?

Do the Balmer series and the Lyman series overlap? Why? Why not? (Hint: calculate the shortest Balmer line and the longest Lyman line.)

A $4.653 -\mu \text{m}$ emission line of atomic hydrogen corresponds to transition between the states $n_{f} = 5$ and $n_{i} .$ Find $n_{i} .$