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# homework 2 - hussain(tsh476 Homework 2 Sutclie(50985 This...

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hussain (tsh476) – Homework 2 – Sutcliffe – (50985) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. This assignment covers the remaining ma- terial that will be in the first 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. If you assume that the uncertainty in your position is large, say about 10 m, and that the car has a mass of 2150 kg, what is the uncertainty in the velocity? 1. 4 × 10 38 m / s 2. 2 . 5 × 10 - 39 m / s correct 3. 5 . 0 × 10 - 38 m / s 4. 1 × 10 33 m 5. 1 × 10 - 39 m / s Explanation: Δ x = 10 m m = 2150 kg Δ v = ¯ h 2 m Δ x = 1 . 055 × 10 - 34 J · s 2 (2150 kg) (10 m) = 2 . 45349 × 10 - 39 m / s 002 10.0 points In a one-dimensional particle in a box, for n = 7, how many WHOLE wavelengths equals the size of the box? 1. 3.5 correct 2. 6 3. 7 4. 14 Explanation: For n = 7 the wavefunction would be x = 0 x = L 003 10.0 points An electron is confined in a 1-dimensional box 3 nm long. Calculate the energy required for it to move from the n = 8 to the n = 9 energy level. 1. 3 . 414 × 10 - 28 J 2. 1 . 138 × 10 - 19 J correct 3. 6 . 694 × 10 - 21 J 4. 5 . 238 × 10 - 19 J 5. 2 . 133 × 10 - 14 J 6. 1 . 717 × 10 - 14 J 7. 2 . 133 × 10 - 19 J Explanation: n 1 = 8 n 2 = 9 h = 6 . 626 × 10 - 34 J · s L = 13 × 10 - 9 m m = 9 . 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 A quantum mechanical particle in a box in its ground state is most likely to be found 1. is equally likely to be found at all positions except the very center of the box. 2. is equally likely to be found at all positions in the box.

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hussain (tsh476) – Homework 2 – Sutcliffe – (50985) 2 3. at both edges of the box. 4. in the middle of the box. correct 5. at the very edge of the box. Explanation: The ground state is Ψ 1 which has maximum probability in the middle of the box. 005 10.0 points For n = 7 and = 4, what is m ? 1. 18 2. 0, 1, 2, 3 3. 9 4. 0, 1, 2, 3, 4 5. - 4, - 3, - 2, - 1, 0, +1, +2, +3, +4 correct Explanation: 006 10.0 points Which of the following sets of quantum num- bers is allowed for an atomic orbital? 1. n = 3, = 1, m = 0, m s = - 1 2 correct 2. n = 2, = 2, m = 1, m s = 1 2 3. n = 3, = 1, m = 2, m s = - 1 2 4. n = 1, = 0, m = 1, m s = 1 2 5. n = 1, = 1, m = 1, m s = 1 Explanation: 007 10.0 points In an atom, the maximum number of electrons having the quantum numbers n = 5 and = 3 is 1. 25.
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