2. If the speed of an electron is measured to within an uncertainty of 2.0×10ª m/s, what woul be the size of the smallest region of space in which the electron can be confined? mẹ = 9.11 × 10-3 kg.
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- Uncertainty Principles 2. (a) Determine the velocity of a bullet measured at 100 m/s, ± 0.001 m/s. If the mass of the bullet is 20g, determine the uncertainty in the bullet's position in meters. (b) Is the uncertainty in position significant in this case.What constraints does the uncertainty principle place on our knowledge of the world? To get a sense of scale, we’ll look at the uncertainty in speed for a confined electron and for a confined dust particle.a. What range of velocities might an electron have if confined toa 0.30-nm-wide region, about the size of an atom?b. A 1.0@mm@diameter dust particle (m ≈ 10-15 kg) is confined within a 5-μm-long box. Can we know with certainty if the particle is at rest? If not, within what range is its velocity likely to be found?8. An electron is trapped within a sphere whose diameter is 5.20 x 10-15 m (about the size of the nucleus of a medium sized atom). What is the minimum uncertainty in the electron's momentum? kg.m/s
- 4. Show that if f= x/y, then the uncertainty in f can be written as: slee + σ y5. An electron ( me = 9.11 × 10−31 kg ) and a bullet ( m = 0.02 kg) each have a velocity of magnitude 500 m/s, with a precision within 0.01%. In what limits is it possible to determine the position of objects along the velocity direction?What can you conclude from comparing your results for the electron and for thebullet?2.3. Find the de Broglie wavelength of (a) an electron, and (b) a proton with speeds of 5 × 106 m/s and compare with the radius of the hydrogen atom, ao. Would either of these particles behave like a wave inside the H atom?
- In a lab a scientist tries to measure the location and speed of an electron. The position measurements are found to have an uncertainty of 5.01 x 10-11 m (this is 0.0501 nm). What is the smallest possible uncertainty in velocity? An electron has a mass of 9.11 x 10-31 kg and Planck's constant is 6.63 x 10-34 J*sRosco the world's biggest magic flying pumpkin. The pumpkin has a mass of: m = 2.5± 0.2 kg Rosco's pumpkin object moves (in space) at a speed of : v = 2.00 ± 0.04 m/s (K = // mv²) SK Figure out the kinetic energy also estimate the uncertainty of rosco's pumpkin andA 83.0 kg athlete running a "4-minute mile" (i.e. 4.00 min/mile) _____ nm an electron (me = 9.10939 1028 g) moving at 3.90 106 m/s in an electron microscope _____ nm.