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.

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

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

The position of a particle which moves along a straight line is defined by: x=t^3-6t^2-15t+40, where x is in feet and t is in seconds. Determine the time at which the velocity will be zero, the positionand distance traveled at that time, and the acceleration of the particle at that time.

(a) Estimate the uncertainty in the momentum of an electron whose location is uncertain by a distance of 2 Angstrom. What is the uncertainty in the momentum of a proton under the same conditions?
(b) What can one conclude about the relative velocities and energies of the electron and proton in the last problem? Are wave phenom

Part 1
A beam of electrons traveling with speed 7 × 10 ^7 m/s passes through a slit of width 1 × 10 ^(-5) m. Because of the uncertainty in the lateral position of the beam, there will be an uncertainty in the transverse momentum as well.
Estimate this uncertainty, and use it to calculate the spread of the image of the elect

5. The Heisenberg uncertainty principle is represented mathematically as deltax × m*deltav = h/2, where deltax is the uncertainty in the position, deltav is the uncertainty in the velocity and h is Planck's constant divided by 2. Would it be possible to develop an instrument that could determine both the positionand velocity

8) The acceleration at time t, of a particle moving along the x axis is given by a(t)=20t^3+6. At time t=0 the velocity of the particle is 0 and the position of the particle is 7. What is the position of the particle at time t?
12) The function f is given by f(x)=3x^2+1. What is the average value os f over the closed inte

Learning Goal: To understand the meaning of the variables that appear in the equations for rotational kinematics with constant angular acceleration.
Rotational motion with a constant nonzero acceleration is not uncommon in the world around us. For instance, many machines have spinning parts. When the machine is turned on or o