General Chemistry 10th Edition

Published by Cengage Learning
ISBN 10: 1-28505-137-8
ISBN 13: 978-1-28505-137-6

Chapter 7 - Quantam Theory of the Atom - Questions and Problems: 7.23

Answer

a) Red light b) Red light has a lover frequency than blue light c) Blue light has more energy than red light d) The speed of both the blue and red lights are the same e) Energy of three photons of same source of blue light will be 3 times the energy of one photon Therefore, energy of 704 nm red light, will be lower than energy of 451 nm blue light. f) Yes g) 1 mole of H2 contains NA (6.022 x 10$^{23}$) electrons ,Therefore they will need NA number of photons to excite them. Difference between energy in 1 and 3 level can be calculated using above formula Energy required in photon = 1.936 x 10$^{-19}$ Therefore wavelength of photon = hc/E = (6.626 x 10$^{-34}$ J*s)(3.0 x 108 m/s) / 1.936 x 10$^{-18}$ J = 1.027 x 10$^{-7}$ m = 1027 angstroms.

Work Step by Step

c) E=$\frac{hc}{wavelength}$ since energy is inversely proportional to wavelength, red light will have lesser energy a compared to blue light d) speed = frequency times the wavelength, since the wavelengths and frequencies of both red and blue light are different in vacuum we can understand that their speed is the same 3*10$^8$. But in other medium blue light has a lower speed than red light. f) it can make transition to higher level as we can calculate it by formula E = -2.178 x 10-18 J (Z$^2$/n$^2$) E = energy, Z = nuclear charge and n = energy level. This equation can be used to calculate the change in energy of an electron when the electron changes orbits
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