Explanation Given data: Energy is given as 3.90 eV. Formula used: Write the expression for wavelength. λ = 1240 eV ⋅ nm Δ E atom (1) Here, Δ E atom is the energy of the atom. Consider the expression of energy. E = E higher − E lower (2) Here, E lower is the energy at lower energy level, and E higher is the energy at higher energy level. Explanation: Refer to Figure 29.24 in the textbook. When there is a transition of light from 3 s to 3 p . E higher for 3 p is 2.10 eV. E lower for 3 s is 0 eV. Substitute 2.10 eV for E higher , and 0 eV for E lower in equation (2), E = 2.10 eV − 0 eV = 2 .10 eV As the energy level is less than 3.90 eV, Substitute 2.10 eV for Δ E atom in equation (1), λ = 1240 eV ⋅ nm 2.10 eV = 590 nm When there is a transition of light from 3 p to 4 s , E higher for 4 s is 3.19 eV E lower for 3 p is 2.10 eV Substitute 3.19 eV for E higher , and 2.10 eV for E lower in equation (2), E = 3.19 eV − 2.10 eV = 1 .09 eV As the energy level is less than 3.90 eV. Substitute 1.09 eV for Δ E atom in equation (1), λ = 1 , 240 eV ⋅ nm 1.09 eV = 1 , 137.6 nm ≅ 1 , 138 nm When there is a transition of light from 3 p to 3 d , E higher for 3 d is 3.62 eV. E lower for 3 p is 2.10 eV. Substitute 3.62 eV for E higher , and 2.10 eV for E lower in equation (2), E = 3.62 eV − 2.10 eV = 1. 52 eV As the energy level is less than 3.90 eV. Substitute 1.52 eV for Δ E atom in equation (1), λ = 1240 eV ⋅ nm 1

College Physics: A Strategic Approach (4th Edition)

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Chapter 29, Problem 42P

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The possible wavelength of light.

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Chapter 29, Problem 41P

Chapter 29, Problem 43P

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An electron with a kinetic energy of 3.90 eV collides with a sodium atom. What possible wavelengths of light are subsequently emitted?

b. An electron and a photon has the same wavelength of 0.21 nm. Calculate the momentum and energy (in eV) of the electron and the photon. (Given c =3.00x108 m s-1, h =6.63 x 1034 J s, me=9.11 x 10-31 kg, mp=1.67 x 1027 kg and e=1.60x1019 C)

A hydrogen atom emits a photon that has momentum 6.977 × 10-27 kg·m/s. This photon is emitted because the electron in the atom falls from a higher energy level into the n = 1 level. What is the quantum number of the level from which the electron falls? Use values of h = 6.626 × 10-34 J·s, c = 2.998 × 108 m/s, and e = 1.602 × 10-19 C.

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College Physics: A Strategic Approach (4th Edition)

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