Explanation The principal quantum number which is denoted by n can take any integer values ( 1 , 2 , 3 , ... ) . The orbital quantum number which is denoted by l can take any integer values from 0 up to n − 1 . Write the expression to obtain the angular momentum of an electron. L = l ( l + 1 ) ℏ (I) Here, L is the angular momentum of an electron, l is the orbital quantum number and ℏ is the numeric value which is the division of Planck’s constant by 2 π . Write the expression to obtain the z component of the angular momentum. L z = m l ℏ (II) Here, L z is the z component of the angular momentum, m l is the magnetic quantum number and ℏ is the numeric value which is the division of Planck’s constant by 2 π . Write the expression to obtain the value of symbol ℏ (“h-bar”). ℏ = h 2 π Here, h is the Planck’s constant. Conclusion: Substitute 6.63 × 10 − 34 J ⋅ s for h in the above equation to calculate ℏ . ℏ = 6.63 × 10 − 34 J ⋅ s 2 π = 1.055 × 10 − 34 J ⋅ s Substitute 1.055 × 10 − 34 J ⋅ s for ℏ and 6.84 × 10 − 34 J ⋅ s for L in equation (I) to calculate l . 6.84 × 10 − 34 J ⋅ s = l ( l + 1 ) ( 1.055 × 10 − 34 J ⋅ s ) l ( l + 1 ) = 6.84 × 10 − 34 J ⋅ s 1.055 × 10 − 34 J ⋅ s Take square both the sides in the above equation

Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780131495081

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

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Chapter 39, Problem 11P

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All the possible values of n, l, and ml.

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Chapter 39 Solutions

Physics for Scientists and Engineers with Modern Physics

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Chapter 39 Solutions