Explanation Formula to calculate the velocity of an electron in the n t h orbit of hydrogen is, v = 2 π k e 2 n h (1) Here, k is the coulomb’s constant ( 9 × 10 9 Nm 2 /C 2 ) . h is the Planck’s constant ( 6.63 × 10 − 34 J .s ) . e is the charge of electron ( 1.6 × 10 − 19 C ) . π = 3.14 . Substitute 2 π k e 2 n h for v in equation (1) to find the ratio v c . v c = 2 π k e 2 n h c (2) Here, c is the velocity of light ( 3 × 10 8 m/s ) . 1 J = 1 Nm Substitute 9 × 10 9 Nm 2 /C 2 for k , 6.63 × 10 − 34 J .s for h , 1.6 × 10 − 19 C for e , 2 for n , 3.14 for π and 3 × 10 8 m/s for c in equation (2) to find the ratio v c

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Chapter 31, Problem 15PCE

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The ratio vc for an electron in the first excited state (n=2) of hydrogen.

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The ratio v c for an electron in the first excited state ( n = 2 ) of hydrogen.

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The ratio vc for an electron in the first excited state (n=2) of hydrogen.

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