Explanation In the ground state of sodium, the outermost electron is in an s state. This state is spherically symmetric, so it generates no magnetic field by orbital motion, and it has same energy no matter about the spin of an electron. The energies of the states 3 p spin up and 3 p spin down above 3 s the energy between the states. Write the expression for energy for the first state. E 1 = h f 1 (I) Here, E 1 is the first state of energy, h is the plank’s constant, and f 1 is the frequency of the first state, Write the expression from the relation between frequency and wavelength. f 1 = c λ 1 (II) Here, λ 1 is the wavelength of the first spectral line and c is the velocity of light. Write the expression for energy for the second state. E 2 = h f 2 (III) Here, E 2 is the second state of energy, h is the plank’s constant, and f 2 is the frequency of the second state, Write the expression from the relation between frequency and wavelength. f 2 = c λ 2 (IV) Here, λ 2 is the wavelength of the second spectral line and c is the velocity of light. Write the expression for energy difference between the two spectral lines. Δ E = E 1 − E 2 (V) Write the expression for energy difference between the two states. Δ E = 2 μ B B (VI) Here, μ B is the Bohr magneton and B is the magnetic field. Conclusion: Substitute equation (II) in equation (I). E 1 = h c λ 1 Substitute equation (IV) in equation (III). E 2 = h c λ 2 Substitute the above two relation in equation (V). Δ E = h c λ 1 − h c λ 2 = h c ( 1 λ 1 − 1 λ 2 ) (VII) Solve the equations (VI) and (VII) to find magnetic field

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Chapter 29, Problem 33P

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Chapter 29, Problem 32P

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Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term

Ch. 29.2 - Prob. 29.1QQ Ch. 29.2 - Prob. 29.2QQ Ch. 29.4 - Prob. 29.3QQ Ch. 29.5 - Prob. 29.4QQ Ch. 29.6 - Prob. 29.5QQ Ch. 29.6 - Prob. 29.6QQ Ch. 29 - Prob. 1OQ Ch. 29 - Prob. 2OQ Ch. 29 - Prob. 3OQ Ch. 29 - Prob. 4OQ

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