Explanation Given Info: The transition is from a p state to an s state. The original wavelength is 575.050 nm , the number of lines after splitting is 3 and the distance between the adjacent lines is 0.0462 nm . Write the equation for the energy of the transition. E = h c λ (1) Here, E is the energy of the transition h is the Planck’s constant c is the speed of light λ is the wavelength The wavelength difference between the adjacent levels is very small and thus the energy is also very small. So we can use the differentials. Differentiate equation (1). d E = − h c λ 2 d λ | d E | = h c λ 2 d λ Δ E = h c Δ λ λ 2 (2) Write the equation for the energy difference between the adjacent lines. Δ E = μ B B (3) Here, μ B is the Bohr magneton B is the value of the magnetic field Put equation (3) in (2). μ B B = h c Δ λ λ 2 Rewrite the equation for B . B = h c Δ λ μ B λ 2 The value h in electron volts is 4.136 × 10 − 15 eV ⋅ s , the value of c is 3.00 × 10 8 m/s and the value of μ B is 5.788 × 10 − 5 eV/T

University Physics with Modern Physics (14th Edition)

14th Edition

ISBN: 9780321973610

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Chapter 41, Problem 41.55P

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The strength of the magnetic field.

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Chapter 41, Problem 41.54P

Chapter 41, Problem 41.56P

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Spectral Analysis. While studying the spectrum of a gas cloud in space, an astronomer magnifies a spectral line that results from a transition from a p state to an s state. She finds that the line at 575.050 nm has actually split into three lines, with adjacent lines 0.0462 nm apart, indicating that the gas is in an external magnetic field. (Ignore effects due to electron spin.) What is the strength of the external magnetic field?

While studying the spectrum of a gas cloud in space, an astronomer magnifies a spectral line that results from a transition from a to an s state. She finds that the line at 575.050 nm has actually split into three lines, with adjacent lines 4.30 x 10-2 nm apart, indicating that the gas is in an external magnetic field. (Ignore effects due to electron spin.) state What is the strength of the external magnetic field? a) O 2.79 T b) 2.98T c) 2.67 T d) 3.08 T e) 3.05 T

F.j = (-e)(-v,k) × (B,i + B.k) ev Bzj. Solving for B gives F. Br 8.50x10 16 N = 1.13 T. Therefore B = 1.13 Ti – 0.772 Tk. The magnitude o A group of particles is traveling in a magnetic field of unknown magnitude and direction. You observe that a proton moving at 1.70 km/s in the +x-direction experiences a force of 2.10x10-16 N in the +y- direction, and an electron moving at 4.70 km/s in the eve (1.60x10 19 C)(4700 m/s) is B = VB? + B = (1.13 T)² + (-0.772 T)² = 1.37 T. -z-direction experiences a force of 8.50x10-16 N in the +y-direction. Part B For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Magnetic force on a proton. What is the direction of the magnetic field? (in the xz-plane) Express your answer in degrees. 0 = 60.59 ° from the -z-direction to the +x-direction Submit Previous Answers Request Answer X Incorrect; Try Again; 9 attempts remaining

Chapter 41 Solutions

University Physics with Modern Physics (14th Edition)

Ch. 41.1 - Prob. 41.1TYU Ch. 41.2 - Prob. 41.2TYU Ch. 41.3 - Prob. 41.3TYU Ch. 41.4 - In this section we assumed that the magnetic field...Ch. 41.5 - In which of the following situations is the...Ch. 41.6 - Prob. 41.6TYU Ch. 41.7 - Prob. 41.7TYU Ch. 41.8 - Prob. 41.8TYU Ch. 41 - Prob. 41.1DQ Ch. 41 - Prob. 41.2DQ

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