The de broglie equation relates the wavelength and the kinetic energy of particles. what is the wavelength, in nanometers, associated with an electron with a speed of 3.42 × 106 m/s? the mass of an electron is 9.109 × 10-31 kg.

0.213 nm

Explanation:

The equation of de Broglie that relates the energy and the wavelength is:

E = h*f

Where h is the plack constant (6.626x10⁻³⁴ J.s), and f is the frequency. The frequency is the speed of light (c) divided by the wavelength (λ).

The wavelength can be calculated then by:

λ = h/mv

Where m is the mass, and v the velocity of the particle. So:

λ = 6.626x10⁻³⁴/(9.109x10⁻³¹x3.42x10⁶)

λ = 2.13x10⁻¹⁰ m

λ = 0.213 nm

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