can you also answer this? What is the de Broglie wavelength (in nm) of a proton traveling at 3.18% of the speed of light?

Question

its a chemistry question.

Answer 1

The de Broglie wavelength shows that matter exhibits wave properties.

λ = h/(m*v)

where λ is wavelength (calculated in meters), h is Planck's constant (6.626 * 10^-34 kg * m²/s), m is the mass of the matter (kg), and v is the (m/s). The velocity in this case is stated as "3.18% of the speed of light". Therefore the equation becomes:

λ = h/(m*0.0318 *c)

where c is the speed of light (m/s).

To solve, the problem is assuming one would be already know the mass of a proton and the speed of light, which could be looked up in reference tables, you would have to memorize, or this would be provided to you....depending on your teacher/class. The mass of a proton is 1.67 × 10^-27 kg. The speed of light is 3.0 x 10⁸ m/s. To solve, then we plug in all the relevant values:

λ = 6.626 * 10^-34 kg * m²/s / (1.67 × 10^-27 kg * 0.0318 3.0 x 10⁸ m/s)

λ = 4.159 * 10^-14 m

Since it asks for in nanometers, multiply the final product by 10 and you get:

λ = 0.0000415