Explanation Write the expression for the angular momentum of the orbit. L = m v r 1 (I) Here, L is the angular momentum of the orbit, r 1 is the radius of the hydrogen atom by the Bohr model , v is the nonrelativistic speed and m is the mass of the electron. Write the expression for the radius of the angular momentum of the orbit. L = n h 2 π (II) Here, n is the quantum number and h is the plank’s constant. Substitute m v r 1 for L in the above equation. m v r 1 = n h 2 π v = h 2 π m r 1 (III) Write the expression for the relativistic factor. 1 − ( v c ) 2 ≈ 1 − ( v c ) 2 (IV) Here, c is the speed of light. Conclusion: Substitute 0.529 × 10 − 10 m for r 1 , 6.63 × 10 − 34 J ⋅ s for h and 9.11 × 10 − 31 kg for m in equation (I) to find the nonrelativistic speed. v = ( 6.63 × 10 − 34 J ⋅ s ) 2 π ( 9

Physics for Scientists and Engineers with Modern Physics

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Chapter 37, Problem 67P

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Whether the use of nonrelativistic formulas are justified in the Bohr atom.

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Chapter 37, Problem 66P

Chapter 37, Problem 68P

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Physics for Scientists and Engineers with Modern Physics

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