Calculate the de Broglie wavelength of an electron travelling at a speed of 2×107 m s−1.

Sure, to calculate the de Broglie wavelength of an electron, we can use the de Broglie equation:

λ = h / p

where:

• λ is the de Broglie wavelength,
• h is the Planck 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 = m * v

where:

• m is the mass of the particle,
• v is the velocity of the particle.

For an electron, the mass m is approximately 9.10938356 × 10^-31 kilograms. The velocity v is given as 2×10^7 m/s.

First, calculate the momentum:

p = m * v p = 9.10938356 × 10^-31 kg * 2×10^7 m/s p = 1.82187671 × 10^-23 kg m/s

Then, substitute p into the de Broglie equation to find λ:

λ = h / p λ = 6.62607015 × 10^-34 m^2 kg / s / 1.82187671 × 10^-23 kg m/s λ = 3.63 × 10^-11 m

So, the de Broglie wavelength of an electron travelling at a speed of 2×10^7 m/s is approximately 3.63 × 10^-11 meters.