CH 301 HW 2 Solutions

# CH 301 HW 2 Solutions - giang(dvg247 Homework 2...

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giang (dvg247) – Homework 2 – Sutclife – (50965) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – Fnd all choices be±ore answering. This assignment covers the remaining ma- terial that will be in the Frst exam. 001 10.0 points You are caught in a radar trap and hope to show that the speed measured by the radar gun is in error due to the uncertainty prin- ciple. I± you assume that the uncertainty in your position is large, say about 10 m, and that the car has a mass o± 2150 kg, what is the uncertainty in the velocity? 1. 5 . 0 × 10 - 38 m / s 2. 4 × 10 38 m / s 3. 1 × 10 - 39 m / s 4. 1 × 10 33 m 5. 2 . 5 × 10 - 39 m / s correct Explanation: Δ x =10m m =2150kg Δ v = ¯ h 2 m Δ x = 1 . 055 × 10 - 34 J · s 2(2150kg)(10m) =2 . 45349 × 10 - 39 m / s 002 10.0 points In a one-dimensional particle in a box, ±or n = 7, how many WHOLE wavelengths equals the size o± the box? 1. 7 2. 3.5 correct 3. 6 4. 14 Explanation: ²or n =7thewave±unctionwou ldbe x =0 x = L 003 10.0 points An electron is conFned in a 1-dimensional box 3nmlong . Ca lcu latetheenergyrequ ired±or it to move ±rom the n =8tothe n =9energy level. 1. 2 . 133 × 10 - 14 J 2. 6 . 694 × 10 - 21 J 3. 3 . 414 × 10 - 28 J 4. 2 . 133 × 10 - 19 J 5. 1 . 138 × 10 - 19 J correct 6. 5 . 238 × 10 - 19 J 7. 1 . 717 × 10 - 14 J Explanation: n 1 =8 n 2 =9 h =6 . 626 × 10 - 34 J · s L =13 × 10 - 9 m m . 109 × 10 - 31 kg Δ E = E n 2 - E n 1 = ( n 2 2 - n 2 1 ) h 2 8 mL 2 = (9 2 - 8 2 )(6 . 626 × 10 - 34 J · s) 2 8(9 . 109 × 10 - 31 kg) (3 × 10 - 9 m) 2 =1 . 13802 × 10 - 19 J 004 10.0 points Aquantummechanicalparticleinaboxinits ground state is most likely to be ±ound 1. in the middle o± the box. correct 2. at both edges o± the box. 3. is equally likely to be ±ound at all positions in the box.

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giang (dvg247) – Homework 2 – Sutclife – (50965) 2 4. at the very edge oF the box. 5. is equally likely to be Found at all positions except the very center oF the box. Explanation: The ground state is Ψ 1 which has maximum probability in the middle oF the box. 005 10.0 points ±or n =7and ± =4,whatis m ± ? 1. - 4, - 3, - 2, - 1, 0, +1, +2, +3, +4 correct 2. 0, 1, 2, 3, 4 3. 0, 1, 2, 3 4. 9 5. 18 Explanation: 006 10.0 points Which oF the Following sets oF quantum num- bers is allowed For an atomic orbital? 1. n =1, ± m ± m s =1 2. n =3, ± m ± =2, m s = - 1 2 3. n ± =0, m ± m s = 1 2 4. n ± m ± m s = 1 2 5. n ± m ± m s = - 1 2 correct Explanation: 007 10.0 points In an atom, the maximum number oF electrons having the quantum numbers n =5and ± =3 is 1. 14. correct 2. 50.
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CH 301 HW 2 Solutions - giang(dvg247 Homework 2...

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