A proton beam is made by accelerating protons in a high voltage electric field. The protons have a velocity of 2.75 x 107 m/s. What is the wavelength of the protons traveling at this very high speed?
I presume this question is after the De Broglie wavelength
so wavelength = h/momentum
where h= Planks constant
and
momentum = mass of proton x velocity.
To find the wavelength of the protons traveling at a given velocity, we can make use of the de Broglie wavelength equation. According to this equation, the wavelength (λ) of a particle is given by the formula:
λ = h / p
where h is the Planck's constant (6.626 x 10^-34 J·s) and p is the momentum of the particle.
The momentum (p) of a proton is given by:
p = mass x velocity
The mass of a proton is approximately 1.67 x 10^-27 kg.
So, plugging in the values into the formula:
p = mass x velocity
= (1.67 x 10^-27 kg) x (2.75 x 10^7 m/s)
= 4.61 x 10^-20 kg·m/s
Now, we can calculate the wavelength:
λ = h / p
= (6.626 x 10^-34 J·s) / (4.61 x 10^-20 kg·m/s)
≈ 1.44 x 10^-14 m
Therefore, the wavelength of the protons traveling at a velocity of 2.75 x 10^7 m/s is approximately 1.44 x 10^-14 meters.