Protons are accelerated to near the speed of light in particle accelerators. What is the wavelength of a proton with a speed of 2.90 x 10^{8} m/s and a mass of 1.673 x 10^{-27} kg?

The wavelength of the proton is 1.3657*10⁻¹⁵ m or 1.3657*10⁻⁹ anstrong

Explanation:

Wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. it is expressed in units of length (m).

In other words, the waves are characterized by having a sinusoidal shape characterized by peaks and valleys. The distance between two peaks of the sine wave is called the wavelength.

 Light is considered as a wave and can also behave as a set of particles (photons). De Broglie stated that matter in general also exhibits this double behavior, that wave-corpuscle duality.

This is reflected by the expression

λ= h/ (m*v)

where m is the mass of the particle, v is the speed with which it moves and the wavelength associated with its movement, and h Planck's Constant (6.626*10⁻³⁴ J s)  

Being:

Replacing and performing the calculations you get:

λ=1.3657*10⁻¹⁵ m

Being 1 anstrong  1*10⁻⁶ m, λ=1.3657*10⁻⁹ anstrong

The wavelength of the proton is 1.3657*10⁻¹⁵ m or 1.3657*10⁻⁹ anstrong

there are two significant figures.