The Bohr Atom
As you learned in class, electrons can absorb energy, become excited and jump to higher energy levels. As the electrons return to lower energy levels, the energy absorbed is released in the form of electromagnetic radiation. If that electromagnetic radiation has a wavelength in the visible range, then we would be able to see it as a color on the spectrum. If the radiation released has longer or shorter wavelength than in the visible range, then we would not able to see it as a line on the spectrum.
In order to calculate the wavelength of the emission, we use the formula:
1/λ= 1.1 x 107 m-1 (1/ni2 – 1/no2)
Where 1.1 x 107 is the Rydberg constant (R), ni= inner energy level and no = outer energy level.
For example, a transition from energy level 2 to energy level 1 would produce an emission with a wavelength of:
1/λ=1.1 x 107 (1 – ¼)= 8.25x 106 so
λ = 1/8.25x 106 = 1.2 x 10-7 m. This emission would have a shorter wavelength than visible light (4.0 x 10-7m to 7.0 x 10 -7 m), and consequently we would not be able to see it as a color. It is in the U.V. region of the electromagnetic spectrum. Transitions to the first energy level make up the Lyman Series.
However, if the transition is to the second energy level, then the wavelength of the emission will be in the visible region. Transitions to the second energy level make up the Balmer Series. For example, from the third to the second energy level.
1/λ= 1.1 x 107 m-1 (1/ni2 – 1/no2)
1/λ=1.1 x 107 (1/22 – 1/32)= 1.5 x 106 so
λ = 1/1.5 x 106 = 6.5 x 10-7 m. This emission is in the visible spectrum and would show as a red line. Transitions to the second energy level are in the visible spectrum.
Finally, if the transition is to the third energy level, then the wavelength of the emission will be longer than visible light and will not be visible. These transitions will be in the infrared region of the electromagnetic spectrum. Transitions to the third energy level make up the Paschen series. For example, if an electron jumps from the fourth energy level to the third, what would be the wavelength of the radiation?
1/λ= 1.1 x 107 m-1 (1/ni2 – 1/no2)
1/λ=1.1 x 107 (1/32 – 1/42)= 5.3 x 105 so
λ = 1/5.3 x 105 = 1.9 x 10-6 m. This emission has a wavelength longer than red and would be in the infrared region.
In conclusion, as the electrons absorb energy, they become excited and jump to higher energy levels. As they return to the ground state, they release the energy they absorbed as electromagnetic radiation, which may or may not be visible. If the electromagnetic radiation emitted has a wavelength from 4.0 x 10-7m to 7.0 x 10 -7 m, then we will be able to see it as a line on the spectrum with the color that corresponds to that wavelength. As the electrons move down to the ground state, they may do so in one or more jumps. For example, an electron that jumped to the third energy level may come down in one jump (from 3-1) or in two jumps (from 3-2 and from 2-1). Each jump releases electromagnetic energy of different wavelengths.
Assignment
- A photon emitted from a sample of hydrogen, as it goes from energy level 4 to 2, has:
- What wavelength (in m)?
- What frequency (in Hz)
- What energy (in J)?
- Is this emission in the U.V., visible, or I.R. region of the E.M. spectrum? If it is in the visible, what is the color?
- A photon emitted from a sample of hydrogen, as it goes from energy level 5 to 2, has:
- What wavelength (in m)?
- What frequency (in Hz)
- What energy (in J)?
- Is this emission in the U.V., visible, or I.R. region of the E.M. spectrum? If it is in the visible, what is the color?
- A photon emitted from a sample of hydrogen, as it goes from energy level 6 to 2, has:
- What wavelength (in m)?
- What frequency (in Hz)
- What energy (in J)?
- Is this emission in the U.V., visible, or I.R. region of the E.M. spectrum? If it is in the visible, what is the color?
- A photon emitted from a sample of hydrogen, as it goes from energy level 5 to 3, has:
- What wavelength (in m)?
- What frequency (in Hz)
- What energy (in J)?
- Is this emission in the U.V., visible, or I.R. region of the E.M. spectrum? If it is in the visible, what is the color?
- A photon emitted from a sample of hydrogen, as it goes from energy level 3 to 1, has:
- What wavelength (in m)?
- What frequency (in Hz)
- What energy (in J)?
- Is this emission in the U.V., visible, or I.R. region of the E.M. spectrum? If it is in the visible, what is the color?
- An electron in a hydrogen atom absorbs energy and jumps to the 4th energy level.
- Describes ALL the possible transitions of the electron as it returns to the ground state.
- Give the wavelength of each emission as it returns to the groups state.
- Which of the transitions will be visible, in which color?
- An electron in hydrogen in an energy level, makes a transition down to the second orbit. If the photon emitted has a wavelength of 4.86 x 10 2 nm, calculate the energy level where the electron was initially.
- In the diagram of a hydrogen atom shown below, draw an arrow to show the jump of an electron that would produce the longest wavelength of visible light?
______n = 6
______n = 5
______n = 4
______n = 3
______n = 2
______n = 1
- In the diagram of a hydrogen atom shown below, draw an arrow to show the jump of an electron that would produce the shortest wavelength of visible light?
______n = 6
______n = 5
______n = 4
______n = 3
______n = 2
______n = 1