Suppose the minimum uncertainty in the position of a particle is equal to its de Broglie wavelength. If the particle has an average speed of 4.5x10^5 m/s, what is the minimum uncertainty in its speed? Units are in m/s.

Solution Summary

This solution discusses the uncertainty principle and calculates the minimum uncertainty with step-by-step workings and explanations.

(a) Show that the kinetic energy of a nonrelativistic particle can be written in terms of its momentum as KE = P2 (squared)/2m. (b) Use the results of (a) to find the minimum kinetic energy of a proton confined within a nucleus having a diameter of 1.0 x 10-15 m.

A helium atom is confined to a one-dimensional space 8 x 10^-10m.
1. What is the minimumuncertainty in the momentum of the helium atom?
2. What is the minimum velocity of the helium atom?
3. What is the minimum energy of the helium atom?

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 velocit

Show that for a free particle, the Uncertainty Principle can be written as
?? ?x ? ?^2/4?
where ?x is the uncertainty in the location of the wave and ?? is the simultaneous uncertainty in the wavelength.

1. The wavelength spectrum of the radiation energy emitted from a system in thermal equilibrium is observes to have a maximum value which decreases with increasing temperature. Outline briefly the significance of this observation for quantum physics.
2. The “stopping potential” in a photoelectric cell depends only on the f

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German physicist Werner Heisenberg related the uncertainty of an object's position (deltax) to the uncertainty in its velocity deltav.
The mass of an electron is 9.11 x 10-31 kg.
What is the uncertainty in the position of an electron moving at 9

An electron of energy 200 eV is passed through a circular hole of radius 10^-4 cm. Find the uncertainty introduced in the angle of emergence? What would be the corresponding uncertainty for a 0.1 g lead ball thrown with a velocity 10^3 cm/s through a hole of 1 cm radius?

What is the approximate uncertainty in the velocity of a proton known to remain within a nucleus of diameter 2.8 * 10^-15 m? What kinetic energy would the proton (mass approximately 1.6 * 10^-27 kg) have at this velocity?

Could you please help me with this question.
By considering the energy-time uncertainty principle, estimate the range of the weak nuclear interaction at low energies. Compare this range to the size of a typical nucleon (for example, a proton) and therefore explain why the weak nuclear interaction between individual nucleons i