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.

Answer:2.1*10^-9 m or 2.1nm

Explanation:

According to De Broglie's equation, the wavelength of any particle is given by wavelength = h/MV

6.6*10^-34/9.109*10^-31*3.42*10^-6

= 2.1*10^-9 m

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