While most transition metals have work functions corresponding to photon frequencies that are larger (higher) than visible light, alkali and alkaline earth metals have low-energy work functions. For example, calcium has a work function of Po = 4.3419×10-19 J. (a) What is the initial state n; for the hydrogen emission lines at visible wavelengths (i.e., those with n = 2) for the lowest-energy photon that would eject an electron from calcium? (b) If the colors of the visible hydrogen emission lines (n; = 3 to n; = 6) are red, green, blue and violet, which colors are capable of ejecting the electrons from calcium? (c) The energy of the emitted photon you identified in part (a), is not identical to the workfunction of calcium. Therefore, the electron is ejected from the metal surface with some kinetic energy (i.e., energy is conserved in the photoelectric effect process). What would the velocity of the electron ejected from calcium (in meters per second)?
While most transition metals have work functions corresponding to photon frequencies that are larger (higher) than visible light, alkali and alkaline earth metals have low-energy work functions. For example, calcium has a work function of Po = 4.3419×10-19 J. (a) What is the initial state n; for the hydrogen emission lines at visible wavelengths (i.e., those with n = 2) for the lowest-energy photon that would eject an electron from calcium? (b) If the colors of the visible hydrogen emission lines (n; = 3 to n; = 6) are red, green, blue and violet, which colors are capable of ejecting the electrons from calcium? (c) The energy of the emitted photon you identified in part (a), is not identical to the workfunction of calcium. Therefore, the electron is ejected from the metal surface with some kinetic energy (i.e., energy is conserved in the photoelectric effect process). What would the velocity of the electron ejected from calcium (in meters per second)?
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Transcribed Image Text:While most transition metals have work functions corresponding to photon frequencies that are
larger (higher) than visible light, alkali and alkaline earth metals have low-energy work functions.
For example, calcium has a work function of Po = 4.3419x10-19 J.
(a) What is the initial state n; for the hydrogen emission lines at visible wavelengths (i.e., those
with nf = 2) for the lowest-energy photon that would eject an electron from calcium?
(b) If the colors of the visible hydrogen emission lines (n; = 3 to n; = 6) are red, green, blue and
violet, which colors are capable of ejecting the electrons from calcium?
(c) The energy of the emitted photon you identified in part (a), is not identical to the
workfunction of calcium. Therefore, the electron is ejected from the metal surface with some
kinetic energy (i.e., energy is conserved in the photoelectric effect process). What would the
velocity of the electron ejected from calcium (in meters per second)?
Expert Solution
Concept and Principle:
The energy of a photon is given by,
Here h is Planck's constant, c is the velocity of light, and λ is the wavelength of the photon.
Now relationship of the energy levels and wavelength is given by,
Here R is the Rydberg constant nf is the final state and ni is the initial state of the electron.
Thus we get the energy equation as,
Now work function is defined as the minimum energy required by a photon to release an electron from the given metal. This means if the photons incident on the material has energy less than work function it won't emit an electron.
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