6.2 The Bohr Model

What model laid the foundation for the quantum mechanical model of the atom?

Bohr model

In the early 20th century, the model of the atom looked like a solar system, with the nucleus being orbited by electrons. However, classical mechanics predicted that the elliptical orbiting electrons should constantly emit light, lose energy, and:

Crash into the nucleus

Early researchers were very excited when they were able to predict the energy of an electron at a particular distance from the nucleus in a hydrogen atom. If a spark promotes the electron in a hydrogen atom into an orbit with n=3, what is the calculated energy, in joules, of the electron?

E = -kZ²/n² k is the energy of the electron at ground state Z is the atomic number of the element n is the energy level E = (-2.179 x 10⁻¹⁸ J) x (1)²/(3)² E = -2.421 x 10⁻¹⁹ J

If a spark promotes the electron in a hydrogen atom into an orbit with n=6, what is the calculated energy, in joules, of the electron?

E = -kZ²/n² k is the energy of the electron at ground state Z is the atomic number of the element n is the energy level E = (-2.179 x 10⁻¹⁸ J) x (1)²/(6)² E = -6.053 x 10⁻²⁰ J

Bohr's model incorporated the inverse relationship between energy and frequency from ______ and quantization from ______.

Einstein, Planck

Bohr's model of the hydrogen atom provides insight into the behavior of matter at the microscopic level, but it does not account for ______ interactions in atoms with more than one electron.

Electron-electron

When an electron transitions from an excited state to a less excited state, or ground state, the difference of energy is:

Emitted as a photon

If an atom receives energy from an outside source, it is possible for the electron to move to an orbit with a higher n value and the atom is now in an ______ with a higher energy.

Excited electronic state

An integer is a whole number; a number that is not a:

Fraction

If a photon is absorbed by an atom, the energy of the photon moves an electron:

From lower energy orbit to a more excited one

The electron of a hydrogen atom usually moves in the n=1 orbit, the orbit in which it has the lowest energy. When the electron is in this lowest energy orbit, the atom is said to be in its:

Ground electronic state

The Bohr model introduced the long-standing feature that an electron's energy ______ with increasing distance from the nucleus.

Increases

The wavelength of the line in the spectrum of hydrogen that represents the movement of an electron from Bohr orbit with n=4 to the orbit with n=6 is 2.62 x 10⁻⁶ m. In what portion of the electromagnetic spectrum is this wavelength from?

Infrared

Quantum numbers are ______ numbers having only specified allowed value and used to characterize the arrangement of electrons in an atom.

Integer

Although Bohr's model explained the hydrogen atom, the model was unable to explain the next simplest atom, helium, which only has two electrons. What was wrong with Bohr's model?

It was still based on the classical mechanics notion of precise orbits which were later discovered to not be true.

One of the fundamental laws of physics is that matter is most stable with the ________ possible energy.

Lowest

In 1913, Niels Bohr ignored the expectation from classical mechanics that orbiting electrons continuously emit light. Bohr assumed that an electron in orbit would not emit any radiation but would release or absorb a photon if it:

Moved to a different orbit

Who won a Nobel Prize in Physics for his contributions to our understanding of the structure of atoms and how that is related to line spectra emissions?

Niels Bohr

The Bohr model introduced the long-standing feature that discrete energies (lines) in the spectra of the elements result from ________ electronic energies.

Quantized

The Bohr model introduced the long-standing feature that the energies of electrons (energy levels) in an atom are quantized, described by _______: integer numbers have only specific allowed value and used to characterize the arrangement of electrons in an atom.

Quantum numbers

As an electron returns to a ground state (say, from n=5 to n=1) the energy can be released as one ______ of energy or two or more smaller ______, as the electrons falls to an intermediate state, then to the ground state.

Quantum, quanta

An atom can _____ energy by using it to promote an electron to a state with higher energy and release it when the electron returns to a lower state.

Store

What feature of the Bohr model is considered to be the most important?

The postulate of quantized energy levels for an electron in an atom.

If a certain amount of external energy is required to excite an electron from one energy level to another, that same amount of energy will be liberated when the electron returns to its initial state. True or False?

True

The classical mechanics description of the atom is incomplete. Since an electron moving in an elliptical orbit would be accelerating (by changing direction) and, according to classical electrodynamics, should continuously emit electromagnetic radiation . The loss of orbital energy should result in the electron's orbit getting smaller until it spirals into the nucleus, implying that atoms are inherently:

Unstable

What is the wavelength of the line in the spectrum of hydrogen that represents the movement of an electron from Bohr orbit with n=4 to the orbit with n=6?

¹/λ = R∞(¹/n₁² - ¹/n₂²) ¹/λ = 1.097 x 10⁷m⁻¹(¹/₄² - ¹/₆²) ¹/λ = 1.097 x 10⁷m⁻¹(0.0347) ¹/λ = 3.81 x 10⁵ m λ = 1/3.81 x 10⁵ m λ =2.62 x 10⁻⁶ m

What is the energy (in joules) of the line in the spectrum of hydrogen that represents the movement of an electron from Bohr orbit with n=4 to the orbit with n=6?

∆E = hc/λ ∆E = (6.626 x 10⁻³⁴ J s) x (2.998 x 10⁸ m s⁻¹)/2.62 x 10⁻⁶m ∆E = 7.58 x 10⁻²⁰ J