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Activity: Using the same emission spectrum at the example. Solve for the frequency of the emitted photon when, an electron of a hydrogen atom drops from energy level Es to energy level E₁ and identify which line corresponds to this event.

Activity: Using the same emission spectrum at the example. Solve for the frequency of the emitted photon when, an electron of a hydrogen atom drops from energy level Es to energy level E₁ and identify which line corresponds to this event.

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Example: An electron in a hydrogen atom drops from energy level E4 to energy level E2. What is the frequency of the emitted photon, and which line in the emission spectrum corresponds to this event? E6 E = -0.378 eV Step 1: Es E = -0.544 eV - E= -0.850 eV Find the energy of the photon. E E = Einitial - Efinal E3 E=-1.51 eV = (-0.850 eV) - (-3.40 eV) = 2.55 eV Step 2: Use Plank's equation for frequency. E₂ E= -3.40 eV 12 E E = hf; f = h (2.55 eV) (1.60 x 10-191 6.63 x 10-34 Js f= 6.15 x 10¹4 Hz Line 3 is in the visible part of the electromagnetic spectrum and appears to be blue. The frequency f = 6.15 x 10¹4 Hz lies within the range of the visible spectrum and is toward the violet end, so it is reasonable that light of this frequency would be visible blue light. Step 3: Find the corresponding line in the emission spectrum. Examination of the diagram shows that the electron's jump from energy level E4 to energy level E2 corresponds to Line 3 in the emission spectrum. 3 Incoming photon Emitted photon (a) (b) Figure 4. (a)When a photon is absorbed by an atom, an electron jumps to a higher energy level. (b)When the electron falls back to a lower energy level, the atom releases a photon. Activity: Using the same emission spectrum at the example. Solve for the frequency of the emitted photon when, an electron of a hydrogen atom drops from energy level Es to energy level E₁ and identify which line corresponds to this event.
Transcribed Image Text:Example: An electron in a hydrogen atom drops from energy level E4 to energy level E2. What is the frequency of the emitted photon, and which line in the emission spectrum corresponds to this event? E6 E = -0.378 eV Step 1: Es E = -0.544 eV - E= -0.850 eV Find the energy of the photon. E E = Einitial - Efinal E3 E=-1.51 eV = (-0.850 eV) - (-3.40 eV) = 2.55 eV Step 2: Use Plank's equation for frequency. E₂ E= -3.40 eV 12 E E = hf; f = h (2.55 eV) (1.60 x 10-191 6.63 x 10-34 Js f= 6.15 x 10¹4 Hz Line 3 is in the visible part of the electromagnetic spectrum and appears to be blue. The frequency f = 6.15 x 10¹4 Hz lies within the range of the visible spectrum and is toward the violet end, so it is reasonable that light of this frequency would be visible blue light. Step 3: Find the corresponding line in the emission spectrum. Examination of the diagram shows that the electron's jump from energy level E4 to energy level E2 corresponds to Line 3 in the emission spectrum. 3 Incoming photon Emitted photon (a) (b) Figure 4. (a)When a photon is absorbed by an atom, an electron jumps to a higher energy level. (b)When the electron falls back to a lower energy level, the atom releases a photon. Activity: Using the same emission spectrum at the example. Solve for the frequency of the emitted photon when, an electron of a hydrogen atom drops from energy level Es to energy level E₁ and identify which line corresponds to this event.
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