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 $8.00\times {10}^6$ m/s. What is the speed of a proton that has the same de Broglie wavelength as this electron?

An alpha particle ($m=6.64\times {10}^{-27}$ 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 $2.80\times {10}^{-10}$ 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 $4.70\times {10}^6$ 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, $v_x$, if the minimum percent uncertainty in a simultaneous measurement of $v_x$ 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 $3.0\times {10}^{-25}$ kg-m/s. Use the Heisenberg uncertainty principle to evaluate the validity of this claim.

The uncertainty in the y-component of a proton's position is $2.0\times {10}^{-12}$ m. What is the minimum uncertainty in a simultaneous measurement of the $y$-component of the proton's velocity?