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HW SOLN 3

# HW SOLN 3 - ECE331 HW#3 Solution 1(a h h 6.63 10-34 kg m p...

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1 ECE331 HW#3 Solution 1. (a) ( ) s m kg x h x p x * 10 06 . 1 10 1 2 10 63 . 6 2 24 10 34 × = × × = Δ = Δ = Δ π π h (b) ( ) s E h E t 1 10 59 . 6 1 2 10 14 . 4 2 16 15 × = × = Δ = Δ = Δ π π h 2) 2 2 1 mv E = , 19 10 6 . 1 1 × = eV 2 1 19 2 1 31 34 10 91 . 4 10 11 . 9 2 10 63 . 6 2 2 × = × × = = = = E E Em h m E m h mv h λ i) For 100eV Α = × = × × = × = 23 . 1 10 23 . 1 10 6 . 1 * 100 10 91 . 4 10 91 . 4 10 19 19 19 100 m E eV λ ii) For 12keV Α = × = × × × = × = 112 . 0 10 12 . 1 10 6 . 1 * 10 12 10 91 . 4 10 91 . 4 11 19 3 19 19 12 m E keV λ For visible light Α = = 5000 5 . 0 um light λ , an electron microscope has much higher resolution 3) At x<0 nm, the probability of finding the electron is zero. At x>6 nm, the probability is non-zero. At x>6 nm, if the electron was described by classical mechanics, this probability is zero. 4) ( ) t y x j e 4 3 10 + Α = Ψ (i) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) h h h h 10 10 4 3 10 4 3 10 * 4 3 10 4 3 10 * 4 3 10 4 3 10 * 4 3 10 4 3 10 * * * = Α Α Α Α = Α Α Α Α = Ψ Ψ Ψ

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HW SOLN 3 - ECE331 HW#3 Solution 1(a h h 6.63 10-34 kg m p...

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