Neutrons traveling at 0.575 m/s are directed through a pair of slits separated by 1.00 mm. A detector screen is placed 10.6 m from the slits.What is the de Broglie wavelength of the neutrons? Use units of metres

To find the de Broglie wavelength of the neutrons, 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 product of its mass and velocity, so:

p = m * v

where: m is the mass of the neutron (1.674927471 × 10^-27 kg), v is the velocity of the neutron (0.575 m/s).

Substituting the values for m and v into the equation for p, we get:

p = (1.674927471 × 10^-27 kg) * (0.575 m/s) = 9.63083420675 × 10^-28 kg m/s

Then, substituting the value for p into the de Broglie equation, we get:

λ = (6.62607015 × 10^-34 m^2 kg / s) / (9.63083420675 × 10^-28 kg m/s) = 6.877 × 10^-10 m

So, the de Broglie wavelength of the neutrons is approximately 6.877 × 10^-10 metres.