Question

A proton in a linear accelerator has a de broglie wavelength of 156 pm . part a what is the speed of the proton?

Answer 1

To calculate the speed of the Proton we use, de Broglie equation as

$\lambda =\frac{h}{mv}$

Here, m is mass of proton and its value of $1.6726219 \times 10^{-27} kg$ and h is Plank constant and its value of $6.626\times 10^{-34} Js$.

Given,  $\lambda = 156 pm = 156 \times 10^{-12} m$ .

Substituting these values in above equation, we get

 $156 \times 10^{-12} m = \frac{6.626\times 10^{-34} Js}{1.6726219 \times 10^{-27} kg\times v} \\\\ v=\frac{3.96\times 10^{-7} }{156 \times 10^{-12} } = 0.02538 \times 10^{5} \ m/s\\\\ v = 2538 \ m/s$

Thus, the speed of proton is 2538 m/s.