Answer to Question #70587 in General Chemistry for lil

Question

What is the wavelength of the matter wave associated with a proton moving at 309 m/s with Earth moving along its orbit around the Sun?

Answer 1

For calculating the proton 's matter wave, which is referred to as the de Broglie wavelength, we need to use her momentum, p and Planck's constant, h, equal to 6,626⋅10−34kg m2s−1. De Broglie wavelength equation is: λ=h/p, where p - the momentum of the proton, λ - her matter wavelength, h - Planck's constant, equal to 6.626⋅10−34J s. The momentum of the proton is directly proportional to its velocity, v, which in your context can be taken to be its speed, and its mass, m. Mass of proton is 1,6726 ⋅ 10-27 kg. Proton momentum: p = m⋅v=1,6726⋅10-27 kg ⋅ 309 ms-1= 5,1684⋅10-25 kg ms-1. Broglie wavelength of proton: 6.626⋅10−34kg m2s−1 / 5,1684⋅10-25 kg ms-1=1,282⋅10-9 m.
Answer: wavelength of the matter is 1,282⋅10-9 m.