(a) An electron moves with a speed of 4.70x10^6 m/s. What is its de Broglie wavelength? (b) A proton moves with the same speed. Determine its de Broglie wavelength.

An electron is moving with a speed of 8.00 * 10^6 m/s. What is the speed of a proton that has the same de Broglie wavelength as this electron?

An alpha particle (m = 6.64x10^-27 kg) emitted in the radioactive decay of uranium-238 has an energy of 4.20 MeV. What is its de Broglie wavelength?

An electron has a de Broglie wavelength of 2.80x10^-10 m. Determine (a) the magnitude of its momentum and (b) its kinetic energy (in joules and in electron volts).

For crystal diffraction experiments (discussed in Section 39.1), wavelengths on the order of 0.20 nm are often appropriate. Find the energy in electron volts for a particle with this wavelength if the particle is (a) a photon.

(a) The x-coordinate of an electron is measured with an uncertainty of 0.30 mm. What is the x-component of the electron's velocity, vx , if the minimum percent uncertainty in a simultaneous measurement of vx is 1.0%? (b) Repeat part (a) for a proton.

A scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultaneously the position of a particle along an axis with a standard deviation of 0.12 nm and its momentum component along this axis with a standard deviation of 3.0x10^-25 kg-m/s. Use the Heisenberg uncertainty principle to evaluate the validity of this claim.

(a) The uncertainty in the y-component of a proton's position is 2.0x10^-12 m. What is the minimum uncertainty in a simultaneous measurement of the y-component of the proton's velocity?

A pesky 1.5-mg mosquito is annoying you as you attempt to study physics in your room, which is 5.0 m wide and 2.5 m high. You decide to swat the bothersome insect as it flies toward you, but you need to estimate its speed to make a successful hit. (a) What is the maximum uncertainty in the horizontal position of the mosquito? (b) What limit does the Heisenberg uncertainty principle place on your ability to know the horizontal velocity of this mosquito? Is this limitation a serious impediment to your attempt to swat it?