Calculate the de Broglie wavelength of an electron moving at 1/137th the speed of light

Sure, to calculate the de Broglie wavelength of an electron moving at 1/137th the speed of light, we need to use the de Broglie equation:

λ = h / p

where: λ is the de Broglie wavelength, h is Planck's constant (6.62607015 × 10^-34 m^2 kg / s), p is the momentum of the particle.

The momentum of a particle is given by the equation:

p = mv

where: m is the mass of the particle, v is the velocity of the particle.

Given that the electron is moving at 1/137th the speed of light, we can substitute c/137 for v, where c is the speed of light (3.00 x 10^8 m/s). The mass of an electron (m) is 9.11 x 10^-31 kg.

So, the momentum (p) of the electron is:

p = (9.11 x 10^-31 kg) * (3.00 x 10^8 m/s / 137) p = 2.00 x 10^-24 kg m/s

Substituting this value into the de Broglie equation gives:

λ = (6.62607015 × 10^-34 m^2 kg / s) / (2.00 x 10^-24 kg m/s) λ = 3.31 x 10^-10 m

So, the de Broglie wavelength of an electron moving at 1/137th the speed of light is approximately 3.31 x 10^-10 meters.