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**Unformatted text preview: **Physics 31 Spring, 2007 Solution to HW #2 Problem A Use the first order Taylor approximation (1 + ) n ≈ 1 + n (for 1) to simplify the following ex- pressions for the indicated limiting cases: (a) M − m M + m for m M (b) 1 λ − 1 λ + ∆ λ for ∆ λ λ (c) p p 2 c 2 + m 2 c 4 for p mc For part (a), M − m M + m = M ³ 1 − m M ´ M ³ 1 + m M ´ = ³ 1 − m M ´³ 1 + m M ´ − 1 ≈ ³ 1 − m M ´³ 1 − m M ´ ≈ 1 − 2 m M For part (b), 1 λ − 1 λ + ∆ λ = 1 λ − 1 λ µ 1 + ∆ λ λ ¶ = 1 λ " 1 − µ 1 + ∆ λ λ ¶ − 1 # ≈ 1 λ · 1 − µ 1 − ∆ λ λ ¶¸ = ∆ λ λ 2 For part (c), as we did in class, p p 2 c 2 + m 2 c 4 = m 2 c 4 µ 1 + p 2 c 2 m 2 c 4 ¶ = mc 2 · 1 + p 2 m 2 c 2 ¸ 1 / 2 ≈ mc 2 · 1 + 1 2 p 2 m 2 c 2 ¸ = mc 2 + p 2 2 m 2 –16 Light of wavelength 400 nm is shone on a metal sur- face in an apparatus like that of Fig. 2.9. The work function of the metal is 2.50 eV. (a) Find the extinction voltage, that is, the retarding voltage at which the photoelectron current...

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