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General Chemistry Principles, Patterns, and Applications, 2011

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Figure 6.11 The Emission of Light by a Hydrogen Atom in an Excited State<br />

(a) Light is emitted when the electron undergoes a transition from an orbit with a higher value of n (at a higher<br />

energy) to an orbit with a lower value of n (at lower energy). (b) The Balmer series of emission lines is due to<br />

transitions from orbits withn ≥ 3 to the orbit with n = 2. The differences in energy between these levels corresponds<br />

to light in the visible portion of the electromagnetic spectrum.<br />

So the difference in energy (ΔE) between any two orbits or energy levels is given by DE = En1- En2 where n1 is<br />

the final orbit <strong>and</strong> n2 the initial orbit. Substituting from Bohr’s equation (Equation 6.9) for each energy value gives<br />

Equation 6.10<br />

DE = Efinal - Einitial = -Rhcn21- (-Rhcn22) = -Rhc(1n21-1n22) If n2 > n1, the transition is from a<br />

higher energy state (larger-radius orbit) to a lower energy state (smaller-radius orbit), as shown by the dashed arrow<br />

in part (a) in Figure 6.11 "The Emission of Light by a Hydrogen Atom in an Excited State". Substituting hc/λ for<br />

ΔE gives<br />

Equation 6.11<br />

DE = hcl = -Rhc(1n21-1n22) Canceling hc on both sides gives<br />

Equation 6.12<br />

1l = -R(1n21-1n22) Except for the negative sign, this is the same equation that Rydberg obtained<br />

experimentally. The negative sign in Equation 6.11 <strong>and</strong> Equation 6.12 indicates that energy is released as the electron<br />

moves from orbit n2 to orbit n1 because orbit n2 is at a higher energy than orbit n1. Bohr calculated the value of 2<br />

independently <strong>and</strong> obtained a value of 1.0974 × 10 7 m − 1, the same number Rydberg had obtained by analyzing the<br />

emission spectra.<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

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