A proton in a linear accelerator has a de Broglie wavelength of 138pm .
What is the speed of the proton?
138 pm = 138E-12 m
wavelength = h/mv
To find the speed of the proton, we can use the de Broglie wavelength formula:
λ = h / (m * v)
Where:
λ is the de Broglie wavelength
h is the Planck's constant (6.626 x 10^-34 Js)
m is the mass of the particle (in this case, the mass of a proton is approximately 1.67 x 10^-27 kg)
v is the velocity of the particle (which is what we are looking for)
Rearranging the formula to solve for v:
v = h / (m * λ)
Now, let's plug in the given values:
λ = 138 pm = 138 x 10^-12 m
Plugging these values into the formula:
v = (6.626 x 10^-34 Js) / (1.67 x 10^-27 kg) / (138 x 10^-12 m)
Calculating:
v = 3.387 x 10^7 m/s
Therefore, the speed of the proton is approximately 3.387 x 10^7 m/s.