Aryan Lowery

2022-10-02

Consider a proton with a 6.6 fm wavelength. What is the velocity of the proton in meters per second? Assume the proton is nonrelativistic. (1 femtometer $={10}^{-15}$ m)

Gabriella Hensley

Beginner2022-10-03Added 6 answers

Wavelength , $\lambda =6.6fm=6.6\times {10}^{-15}m$

To find = Velocity of proton

We can calculate the velocity using :

De Broglie wave equation :

$\lambda =\frac{h}{mv}$ , where h is Planck's constant and m is proton's mass .

Solving for v , we get :

$v=\frac{h}{m\lambda}$, where $m=1.67\times {10}^{-27}kg,h=6.626\times {10}^{-34}Js$

Substituting the given values ,we get :

$v=\frac{6.626\times {10}^{-34}}{1.67\times {10}^{-27}\times 6.6\times {10}^{-15}}$

$v=0.6\times {10}^{8}$

$v=6\times {10}^{7}$ m/s

Hence ,the velocity of the proton is $v=6\times {10}^{7}$ m/s .

To find = Velocity of proton

We can calculate the velocity using :

De Broglie wave equation :

$\lambda =\frac{h}{mv}$ , where h is Planck's constant and m is proton's mass .

Solving for v , we get :

$v=\frac{h}{m\lambda}$, where $m=1.67\times {10}^{-27}kg,h=6.626\times {10}^{-34}Js$

Substituting the given values ,we get :

$v=\frac{6.626\times {10}^{-34}}{1.67\times {10}^{-27}\times 6.6\times {10}^{-15}}$

$v=0.6\times {10}^{8}$

$v=6\times {10}^{7}$ m/s

Hence ,the velocity of the proton is $v=6\times {10}^{7}$ m/s .

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