7.1.6 The Bohr Model

Question 1

The Bohr Model

Answer 1

• The Bohr model provided the conceptual bridge from classical theoretical physics to quantum mechanics. It is important because it introduced the idea of quantized energy states for electrons in atoms.
• Bohr’s model worked very well for explaining atoms and ions having a single electron, such as H, He + , Li 2+, and Be 3+ .
• Bohr’s model was inadequate for explaining atomic spectra of other atoms or ions.

Question 2

note

Answer 2

• Neils Bohr explained the observation that the missing
  spectral frequencies of sunlight are exactly the same
  frequencies as those emitted by the hydrogen atom.
• The Bohr model provided the conceptual bridge from classical theoretical physics to quantum mechanics. It is important because it introduced the idea of quantized energy states for electrons in atoms.
• Bohr’s postulated that the angular momentum of electrons is quantized, so the distance of electrons from the nucleus is quantized, and the energy of electrons is quantized.
• The Bohr model asserted that only certain orbits were
  allowed. It accounted for potential energy, kinetic energy, and the fact that only specific energy levels were observed. It also stated that energy was directly proportional to the square of the nuclear charge divided by the square of the principal quantum number, which must be a positive integer.
• The Bohr model explained all lines in both the visible and the non-visible spectra of hydrogen (the Balmer series, the Lyman series, and the Paschen series).
• While the Bohr model works well for predicting properties of hydrogen, it does not work for elements with more than one electron.
• The Bohr model assumed that the electron was a particle with a fixed distance from the nucleus.
• However, just like light, electrons have both particle
  properties and wave properties.

Question 3

The emission spectrum of which of the following atoms or ions could not be predicted by the Bohr model?

Answer 3

a neutral isotope of helium containing one neutron

Question 4

What can you conclude from the fact that the emission spectrum of hydrogen corresponds to the Fraunhofer lines in sunlight?

Answer 4

Sunlight passes through hydrogen gas before it reaches Earth.

Question 5

In the visible absorption spectrum of a gas sample, certain discrete frequencies are missing. What do these missing frequencies represent?

Answer 5

Frequencies which cause the electrons of the gas to move to higher energy levels

Question 6

Which of the following transitions of an electron in a hydrogen atom will emit the longest wavelength of light?

Answer 6

from n = 5 to n = 3

Question 7

Suppose an electron with a quantum number of n = 3 absorbs a photon with energy of 1.55 × 10^−19 J and then emits a photon with energy of 4.58 × 10^−19 J. What is the final quantum number of the electron after emission?

Answer 7

2

Question 8

What frequency of light will be emitted from a lithium ion (Li 2+ ) when its electron drops from an energy level of n = 5 to an energy level of n = 2?

Answer 8

6.22 × 10^15 s−1

Question 9

How much energy must an electron in a hydrogen atom absorb to move from the first (or lowest) energy level to the third energy level?

Answer 9

1.94 × 10^−18 J

Question 10

Hydrogen gas emits four lines in the visible region of the spectrum (at 410 nm, 434 nm, 486 nm, and 656 nm). Which of the following best explains why hydrogen does not emit light with a wavelength of 680 nm?

Answer 10

No two energy levels are separated by a difference corresponding to a 680 nm photon.

Question 11

According to the Bohr model of the atom, when does the energy of an electron in an atom decrease?

Answer 11

When the charge of the nucleus increases or the quantum number n decreases

Question 12

There are four Fraunhofer lines in the visible portion of the solar spectrum that correspond to the emission spectrum of hydrogen gas. However, scientists have discovered approximately 25,000 dark lines in the complete solar spectrum (one that includes the visible and the invisible portions). What can you conclude based on this information?

Answer 12

The sun’s atmosphere contains a variety of gases.