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# Calculating Minimum Resulting Uncertainty and Minimum Kinetic Energy

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Part 1
Suppose optical radiation (of wavelength 2.6 × 10^-7 m) is used to determine the position of an electron to within the wavelength of the light. The mass of an electron is 9.10939 × 10^-31 kg and the Planck's constant is 6.62607 × 10^-34 J · s.
What will be the minimum resulting uncertainty in the electron's velocity?

Part 2
We wish to measure simultaneously the wavelength and position of a photon.
Assume that the wavelength measurement gives lamba = 4673 x 10^-10 with an accuracy of delta lambda/lamda = 5.9 × 10^-6 .

What is the minimum uncertainty in the position of the photon? Use propagation of uncertainties and the uncertainty in lambda to calculate the uncertainty in the momentum.

Part 3
The kinetic energy of a nonrelativistic particle can be written in terms of its momentum as
K = p ^2 /2 m .
Planck's constant is 6.63 × 10^-34 J · s.
What is the minimum kinetic energy of a proton confined within a nucleus having a diameter of 6 × 10^-16 m?