userdata-paziras-Chem101-Chap_07A

Whatisthedifference inenergy

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Unformatted text preview: mo lecules will make one atom gain energy fro m another, by mo ving the electron from the lowest energy level (E1) to a higher level (for example E2) E2 (final) Energy absorbed = Ef - Ei = E2 - E1 = hn e E1 (init ial) Transition of the electron in the H atom 12 Chemistry 101 Chapter 7 Using the concept of electron transit ions, Bohr was able to reproduce Rydberg’s (Balmer’s) equation: Energy of initial energy level = Ei RH Ei = - ¾¾ ni 2 Energy of final energy level = Ef RH Ef = - ¾¾ nf2 ni = principal quantum number for the init ial energy level nf = pr incipal quantum number for the final energy level Energy o f the emitted photon = hυ = E ­ E = (­ i f hυ = R H R H 1 1 ­ 2 = R H ( 2 ­ 2 ) 2 n ni n n i f f Recall: c = u l h R H R H ) ­ (­ 2 ) 2 n i n f and c 1 1 = R H ( 2 ­ 2 ) λ n n i f therefore υ = By rearrangement: c λ 1 R 1 1 = H ( 2 ­ 2 ) λ hc n n i f By subst ituting: RH = 2.179 x 10 18 J h = 6.63 x 10 34 J.s 1 1 1 = 1.097 x 107 ( 2 ­ 2 ) m ­1 λ nf n i 13 8 c = 3.00 x10 m/s RYDBERG’S GENERALIZED EQUATION IS OBTAINED. Chemistry 101 Chapter 7 Examples: 1. An electron in a hydrogen atom in the level n = 5 undergoes a transit ion to level n = 3. What is the frequency of the emitted radiat ion? 1 1 1 = 1.097 x 107 ( 2 ­ 2 ) m ­1 λ nf n i ni = 5 nf = 3 1 1 1 ­ = 1.097 x 107 ( 2 ­ 2 ) m 1 λ 3 5 l = ??? l = u = ??? υ = c λ 2. What is the difference in energy between the two levels responsible for the vio let emissio n line of the calcium atom at 422.7 nm? l = 422.7 nm x ¾¾¾¾ = m υ = c = λ E = h u = 14 Chemistry 101 Chapter 7 QUANTUM MECHANICS · Quantum mechanics is a theory that applies to extremely small particles, such as electrons. DUAL NATURE OF...
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