HW2 - padilla(tp5647 Homework 2 Sutclie(53770 This...

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padilla (tp5647) – Homework 2 – Sutcliffe – (53770) 1 This print-out should have 27 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Calculate the velocity of an oxygen molecule if it has a de Broglie wavelength of 0.0140 nm. 1. 8.9 m/s 2. 891 m/s correct 3. 1780 m/s 4. 3 × 10 8 m/s 5. 445 m/s Explanation: λ = 0 . 0140 nm = 1 . 4 × 10 11 m m = 32 g / mol 6 . 022 × 10 23 = 5 . 31385 × 10 23 g = 5 . 31385 × 10 26 kg λ = h m v v = h m λ = 6 . 626 × 10 34 J · s 5 . 31385 × 10 26 kg × 1 1 . 4 × 10 11 m = 890 . 665 m / s 002 10.0 points (Note this is the deBroglie wavelength) The average speed of a helium atom at 25 C is 1 . 23 × 10 3 m / s. What is the average wave- length of a helium atom at this temperature? 1. 4 . 15 × 10 12 m 2. 2 . 03 × 10 11 m 3. 8 . 11 × 10 11 m correct 4. 7 . 43 × 10 15 m 5. 4 . 06 × 10 11 m Explanation: v = 1 . 23 × 10 3 m / s The mass of one He atom is mass He = 4 . 00 g / mol 6 . 022 × 10 23 atoms / mol = 6 . 64 × 10 24 g = 6 . 64 × 10 27 kg Using de Broglie’s relationship, λ = h p = h m v = 6 . 626 × 10 34 kg · m 2 / s (6 . 64 × 10 27 kg) (1230 m / s) = 8 . 11294 × 10 11 m 003 10.0 points Estimate the minimum uncertainty in the po- sition of an electron of mass 9 . 109 × 10 31 kg if the error in its speed is 3 × 10 5 m / s. 1. 1 . 93 × 10 12 m 2. 193 pm correct 3. 386 pm 4. 386 × 10 12 m Explanation: m = 9 . 109 × 10 31 kg Δ v = ± 3 × 10 5 m / s Δ x = ¯ h 2 m Δ v = 1 . 055 × 10 34 J · s 2 (9 . 109 × 10 31 kg) (3 × 10 5 m / s) = (1 . 93033 × 10 10 m) parenleftbigg 10 12 pm 1 m parenrightbigg = 193 . 033 pm . 004 10.0 points
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padilla (tp5647) – Homework 2 – Sutcliffe – (53770) 2 In a hydrogen atom which transition would emit the longest wavelength light? 1. n = 2 to n = 4 2. n = 5 to n = 4 correct 3. n = 5 to n = 3 4. n = 2 to n = 1 5. n = 4 to n = 3 6. n = 1 to n = 2 Explanation: To emit the first level needs to be higher energy than the second level. The longest wavelength will be lowest frequency. This will come from the two levels that are closest together. This is the n = 5 to n = 4 transition. 005 10.0 points Which of the following provided evidence that the electrons in atoms are arranged in distinct energy levels? 1. the results of the Millikan oil-drop exper- iment 2. the observation of line spectra from gas discharge tubes correct 3. the deflection of ions in a mass spectrom- eter 4. the scattering of α particles by a metal foil 5. the existence of elements with noninteger values for atomic weights Explanation: The fact that gases emitted only specific wavelengths of energy suggested that electron energy states are quantized.
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