A proton in a linear accelerator has a de Broglie wavelength of 115pm. What is the speed of the proton?
wavelength in m = h/mv
h is Plancks constant
m is mass proton in kg
v is velocity in m/s
how would you find out the mass?
Go to Google, type in mass proton. Or look in your text/notes.
3.5^3
To determine the speed of the proton, we can use the de Broglie equation, which relates the wavelength (λ) of a particle to its mass (m) and velocity (v).
The de Broglie equation is given by:
λ = h / (m * v)
Where:
λ is the de Broglie wavelength of the particle
h is the Planck's constant (approximately 6.626 x 10^-34 J·s)
m is the mass of the particle
v is the velocity of the particle
In this case, we are given the de Broglie wavelength (λ = 115 pm) and we need to find the velocity (v) of the proton. The mass of a proton is approximately 1.67 x 10^-27 kg.
Substituting the given values into the equation:
115 pm = (6.626 x 10^-34 J·s) / (1.67 x 10^-27 kg * v)
We can solve for v by rearranging the equation:
v = (6.626 x 10^-34 J·s) / (1.67 x 10^-27 kg * 115 pm)
Before substituting the values, we need to convert the wavelength from picometers (pm) to meters (m) as the SI units for mass (kg) and velocity (m/s):
1 pm = 1 x 10^-12 m
Now, let's substitute the values and calculate the velocity:
v = (6.626 x 10^-34 J·s) / (1.67 x 10^-27 kg * 115 pm)
= (6.626 x 10^-34 J·s) / (1.67 x 10^-27 kg * 115 x 10^-12 m)
= (6.626 x 10^-34 J·s) / (1.92 x 10^-17 kg·m)
≈ 3.44 x 10^6 m/s
Therefore, the speed of the proton is approximately 3.44 x 10^6 m/s.