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.

Calculate the de Broglie wavelength of a 5.00-g bullet that is moving at 340 m/s. Will the bullet exhibit wavelike properties?

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).

(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.

(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?