Question

Find the wavelength of a proton moving at 1.00 % of the speed of light.

Short answer

The wavelength of a proton is obtained as \[1.32 \times {10^{ - 13}}\;{\rm{ma}}\].

Step-by-step solution

Define formula for the wavelength.

Consider the formula for the proton is:

\[\lambda = \frac{h}{{mv}}\]

Here, h is the plank’s constant, v is the velocity of the photon and m is the mass of the proton.

Evaluate the wavelength

Substitute the values and solve for the wavelength as:

\[\begin{array}{c}\lambda = \frac{{6.63 \times {{10}^{ - 34}}\;{\rm{J}} \cdot {\rm{s}}}}{{1.67 \times {{10}^{ - 27}}\;{\rm{kg}} \times 0.01 \times 3.00 \times {{10}^8}\;\frac{{\rm{m}}}{{\rm{s}}}}}\\ = 1.32 \times {10^{ - 13}}\;{\rm{m}}\end{array}\]

Therefore, the wavelength is\[{\rm{1}}{\rm{.32}} \times {\rm{1}}{{\rm{0}}^{ - {\rm{13}}}}{\rm{ m}}\].