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: 7.31

Answer

n = 4

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 Ground state. And, the wavelength of the absorbed photon is 97.20 nm. So, n1 = ground state = 1 λ = 97.20 nm Unknowns : The unknown quantity is the final Energy level of the electron n2 = ? 3 Solution : Substituting the values in the Rydberg's formula, 1/ 97.20 x 10^-9 = 1.0967 x 10^7 [1/(1)² - 1/(n2)²] 1 - (1/n2)² = 0.938 (1/n2)² = 0.062 (n2)² = 16 .... (approx) n2 = 4 .... (approx) Thus, the given electron will move to an energy level of n = 4.
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