Question

Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in nm) of such a proton moving at 2.90 × 108 m/s (mass of a proton = 1.673 × 10−27 kg). Enter your answer in scientific notation.

Answer 1

Given info : protons can be accelerated to speed near that of light in particle accelerators.

To find : the wavelength of such a proton moving at 2.90 × 10⁸ m/s is ..

solution : as proton is a particle, we should De-broglie's wavelength equation of subatomic particle.

we know, λ = h/p = h/mv

here, mass of proton, m = 1.673 × 10⁻²⁷ kg

velocity of proton, v = 2.90 × 10⁸ m/s

now, λ = (6.63 × 10⁻³⁴ Js)/(1.673 × 10⁻²⁷ × 2.90 × 10⁸)

           = (6.67)/(1.673 × 2.90) × 10⁻¹⁵

           = 1.375 × 10⁻¹⁵ m

therefore the wavelength of the proton is 1.375 × 10⁻¹⁵