9. Quantum Mechanics

Bohr Equation

9. Quantum Mechanics

Bohr Equation

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Bohr Equation Example 1

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08:10

How to... Draw Bohr Models

Louis de Broglie's explanation of Bohr's atomic model

Crash Chemistry Academy

Practice Problem: The Bohr Model and Photon Wavelength

Professor Dave Explains

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03:37

Deriving the Bohr Radius of the Atom

Bohr Model of the Hydrogen Atom

Professor Dave Explains

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Practice this topic

Multiple Choice

What is the wavelength of a photon (in nm) absorbed during a transition from the n = 2 to n = 5 state in the hydrogen atom?

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Multiple Choice

Determine the end (final) value of n in a hydrogen atom transition, if the electron starts in n = 5 and the atom releases a photon of light with an energy of 4.5738 × 10^-19 J.

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Multiple Choice

An electron releases energy as it moves from the 6^th shell to the 3^rd shell. If it releases 4.25 x 10⁹ kJ of energy at a wavelength of 915.7 nm, how many photons were released in the process?

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Textbook Question

Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. (c) Calculate the wavelength of the photon emitted for each transition. Do any of these transitions lead to the emission of visible light? If so which one(s)?

Calculate the wavelength of the photon emitted for transition B.

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Textbook Question

Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. (b) Calculate the energy of the photon emitted for each transition.

Calculate the energy of the photon emitted for transition C.

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Textbook Question

Calculate the wavelength in nm of the light emitted when an electron makes a transition from an orbital in n = 5 to an orbital in n = 2 in the hydrogen atom. (LO 5.8) (a) 2.31 * 10-3 nm (b) 4.34 * 10-2 nm (c) 231 nm (d) 434 nm

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Textbook Question

The visible emission lines observed by Balmer all involved nf = 2. (b) Calculate the wavelengths of the first three lines in the Balmer series—those for which ni = 3, 4, and 5—and identify these lines in the emission spectrum shown in Figure 6.11.

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Textbook Question

The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (b) Calculate the wavelengths of the first three lines in the Lyman series—those for which ni = 2, 3, and 4.

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Textbook Question

One of the emission lines of the hydrogen atom has a wavelength of 94.974 nm. (b) Determine the initial and final values of n associated with this emission.

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Textbook Question

Order the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed: n = 3 to n = 7, n = 4 to n = 8, n = 2 to n = 5, and n = 1 to n = 3.

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Textbook Question

Calculate the wavelength and energy in kilojoules necessary to completely remove an electron from the second shell (m = 2) of a hydrogen atom (R∞ = 1.097 * 10-2 nm-1).

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Textbook Question

Use the Balmer equation to calculate the wavelength in nano-meters of the spectral line for hydrogen when n = 6 and m = 2. What is the energy in kilojoules per mole of the radiation corresponding to this line?

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Textbook Question

Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes each transition and indicate the region of the electromagnetic spectrum (infrared, visible, ultraviolet, etc.) where the light is found. a. n = 2¡n = 1 b. n = 3¡n = 1 c. n = 4¡n = 2 d. n = 5¡n = 2

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Textbook Question

Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each transition: a. n = 4¡n = 3 b. n = 5¡n = 1 c. n = 5¡n = 4 d. n = 6¡n = 5

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Textbook Question

An electron in the n = 7 level of the hydrogen atom relaxes to a lower-energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?

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Textbook Question

An electron in a hydrogen atom relaxes to the n = 4 level, emitting light of 114 THz. What is the value of n for the level in which the electron originated?

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Textbook Question

An atomic emission spectrum of hydrogen shows three wavelengths: 1875 nm, 1282 nm, and 1093 nm. Assign these wavelengths to transitions in the hydrogen atom.

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Textbook Question

An atomic emission spectrum of hydrogen shows three wavelengths: 121.5 nm, 102.6 nm, and 97.23 nm. Assign these wavelengths to transitions in the hydrogen atom.

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Textbook Question

Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = . (d) How are the results of parts (b) and (c) related to the plot shown in Exercise 6.88?

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Textbook Question

Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = . (b) What is the wavelength of light that must be absorbed to accomplish this process?

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Textbook Question

Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = . (a) What is the end result of this transition?

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Textbook Question

The series of emission lines of the hydrogen atom for which nf = 4 is called the Brackett series. (b) Calculate the wavelengths of the first three lines in the Brackett series—those for which ni = 5, 6, and 7.

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Textbook Question

Orbital energies in single-electron atoms or ions, such as He+, can be described with an equation similar to the Balmer–Rydberg equation:

where Z is the atomic number. What wavelength of light in nanometers is emitted when the electron in He+ falls from n = 3 to n = 2?

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Textbook Question

In the Bohr model of atomic structure, electrons are constrained to orbit a nucleus at specific distances, given by the equation

where r is the radius of the orbit, Z is the charge on the nucleus, a0 is the Bohr radius and has a value of 5.292 * 10-11 m, and n is a positive integer (n = 1, 2, 3...) like a principal quantum number. Furthermore, Bohr concluded that the energy level E of an electron in a given orbit is

where e is the charge on an electron. Derive an equation that will let you calculate the difference ∆E between any two energy levels. What relation does your equation have to the Balmer–Rydberg equation?

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Textbook Question

(b) What wavelength of light is emitted by the process?

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Textbook Question

(c) The hydrogen atom now has a single electron in the 3d subshell. What is the energy in kJ>mol required to remove this electron?

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Textbook Question

(c) The energy required to completely remove the outermost electron from the excited xenon atom is 369 kJ/mol, almost identical to that of cesium (376 kJ/mol). Explain.

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Open Question

Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each of the following transitions.

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Open Question

Which wavelength in the hydrogen emission spectrum corresponds to the transition from n=5 to n=2?

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Open Question

If our eyes could see a slightly wider region of the electromagnetic spectrum, we would see a fifth line in the Balmer series emission spectrum. Calculate the wavelength λ associated with the fifth line.

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Open Question

Calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from 𝑛=6 to 𝑛=1.

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Open Question

What is the frequency of light that corresponds to the transition of the electron from the n = 3 to the n = one state of the hydrogen atom?

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Open Question

Determine the energy change associated with the transition from n = 2 to n = 5 in the hydrogen atom.

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Open Question

An electron in the n = 7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. what is the value of n for the level to which the electron relaxed?

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Open Question

What is the wavelength λ of the photon that has been released in part b?

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Open Question

What is the value of n for the level in which the electron originated?

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