# 6.4 Bohr’s model of the hydrogen atom  (Page 9/37)

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## Conceptual questions

Explain why the patterns of bright emission spectral lines have an identical spectral position to the pattern of dark absorption spectral lines for a given gaseous element.

Do the various spectral lines of the hydrogen atom overlap?

no

The Balmer series for hydrogen was discovered before either the Lyman or the Paschen series. Why?

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?

They are at ground state.

Hydrogen accounts for about 75% by mass of the matter at the surfaces of most stars. However, the absorption lines of hydrogen are strongest (of highest intensity) in the spectra of stars with a surface temperature of about 9000 K. They are weaker in the sun spectrum and are essentially nonexistent in very hot (temperatures above 25,000 K) or rather cool (temperatures below 3500 K) stars. Speculate as to why surface temperature affects the hydrogen absorption lines that we observe.

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

Discuss the way in which Thomson’s model is nonphysical. Support your argument with experimental evidence.

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?

increase

How is the energy conserved when an atom makes a transition from a higher to a lower energy state?

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

for larger n

Discuss why the allowed energies of the hydrogen atom are negative.

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

Yes, the excess of 13.6 eV will become kinetic energy of a free electron.

Why can you see through glass but not through wood?

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

no

Show that Planck’s constant has the dimensions of angular momentum.

## Problems

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

121.5 nm

Calculate the wavelength of the fifth 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 $n=\infty .$

a. 0.661 eV; b. –10.2 eV; c. 1.511 eV

Determine the wavelength of the third Balmer line (transition from $n=5$ to $n=2$ ).

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

3038 THz

When a hydrogen atom is in its ground state, what are the shortest and longest wavelengths of the photons it can absorb without being ionized?

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

97.33 nm

What is the longest wavelength that light can have if it is to be capable of ionizing the hydrogen atom in its ground state?

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.

a. h/ $\pi ;$ b. 3.4 eV; c. – 6.8 eV; d. – 3.4 eV

Find the ionization energy of a hydrogen atom in the fourth energy state.

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?

$n=4$

What is the radius of a hydrogen atom when the electron is in the first excited state?

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

365 nm; UV

Show that the entire Paschen series lies in the infrared part of the spectrum.

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

no

(a) Which line in the Balmer series is the first one in the UV part of the spectrum? (b) How many Balmer lines lie in the visible part of the spectrum? (c) How many Balmer lines lie in the UV?

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

7

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