## Physics for Scientists

Physics & Astronomy

## Quiz 39 :

Wave Functions and Uncertainty

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Q08 Q08 Q08

A molecule of roughly spherical shape has a mass of 6.10 × 10

^{-25}kg and a diameter of 0.70 nm. The uncertainty in the measured position of the molecule is equal to the molecular diameter. What is the minimum uncertainty in the speed of this molecule? (h = 6.626 × 10^{-34}J ∙ s)Free

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Multiple Choice

Q09 Q09 Q09

A nonrelativistic electron is confined to a length of 500 pm on the x-axis. What is the kinetic energy of the electron if its speed is equal to the minimum uncertainty possible in its speed? (h = 6.626 × 10

^{-34}J ∙ s, m_{el}= 9.11 × 10^{-31}kg, 1 eV = 1.60 × 10^{-19}J)Free

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Multiple Choice

Q10 Q10 Q10

A nonrelativistic proton is confined to a length of 2.0 pm on the x-axis. What is the kinetic energy of the proton if its speed is equal to the minimum uncertainty possible in its speed? (1 eV = 1.60 × 10

^{-19}J, h = 6.626 × 10^{-34 }J ∙ s, m_{proton}= 1.67 × 10^{-27}kg)Free

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Multiple Choice

Q11 Q11 Q11

A small dust particle of mass 7.90 × 10

^{-6}g is being observed under a magnifying lens. Its position is determined to within 0.0050 mm. (1 y = 3.156 × 10^{7}s, h = 6.626 × 10^{-34}J ∙ s) (a) Find the minimum uncertainty in its velocity implied by the uncertainty in its position. (b) Assuming the dust particle is moving at the speed you just found, how many years would it take for the particle to move 1.0 mm?Free

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Essay

Q17 Q17 Q17

A particle is confined to a one-dimensional box (an infinite well) on the x-axis between x = 0 and x = L. The potential height of the walls of the box is infinite. The normalized wave function of the particle, which is in the ground state, is given by ψ(x) = sin , with 0 ≤ x ≤ L. What is the probability of finding the particle between x = 0 and x = L/3?

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Multiple Choice

Q18 Q18 Q18

A particle is confined to a one-dimensional box (an infinite well) on the x-axis between x = 0 and x = L. The potential height of the walls of the box is infinite. The normalized wave function of the particle, which is in the ground state, is given by ψ(x) = sin , with 0 ≤ x ≤ L. What is the maximum probability per unit length of finding the particle?

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Multiple Choice