Chemistry: The Molecular Nature of Matter and Change 7th Edition

Published by McGraw-Hill Education
ISBN 10: 007351117X
ISBN 13: 978-0-07351-117-7

Chapter 7 - Problems: 7.32

Answer

n=3

Work Step by Step

1 Analysis : Rydberg's Equation is given as : 1/ λ = R [1/(n1)² - 1/(n2)²] Where, λ : Wavelength R : Rydberg's Constant = 1.0967 x 10^7 / m n1 & n2 : Positive constants corresponding to the energy levels involved. 2 Knowns : Here, it is given that the Hydrogen atom is in it's 5th state, and the wavelength of the emitted photon is 1281 nm. So, n2 = 5 λ = 1281 nm = 1281 x 10^-9 m = 1.281 x 10^-6 m Unknowns : The unknown quantity is the final Energy level of the electron n1 = ? 3 Solution : Substituting the values in the Rydberg's formula, 1/ 1.281 x 10^-6 = 1.0967 x 10^7 [1/(n1)² - 1/(5)²] 1 / 14.048 = 1/(n1)² - 1/(5)² (1/n1)² = 0.111 (n1)² = 9.09 n1 = 3 .... (approx) Thus, the given electron will move to an energy level of n = 3.
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