Determine the wavelength of an electron that has a kinetic energy of 1.15 × 10^{-19} J. Report your answer in units of nm to the correct number of significant figures.

The electron has a wavelength of 1448 nanometers.

Explanation:

The wavelength of the electron can be determined by means of the de Broglie wavelength.

 (1)

Where h is the Planck's constant and p is the momentum

(2)

The velocity can be found by means of the kinetic energy equation.

(3)

Therefore, equation 3 can be replaced in equation 2

(4)

Where m is the mass of the electron and KE its kinetic energy.

But

Finally,  the wavelength can be expressed in terms of nanometers:

⇒

Hence, the electron has a wavelength of 1448 nanometers.

gas and liquid