If a proton were traveling the same speed as electrons in a TV picture tube (about 7.2 107 m/s), what would its de Broglie wavelength be? The mass of a proton is 1.67 10-27 kg.
The De Broglie wavelength can be calculated by...
λ = h/p
or
λ = h/mv
So, plug the numbers in and...
λ = (6.63 x 10^-34 J*s) / [(1.67 x 10^-27 kg)(7.2 x 10^7 m/s)]
λ = 5.5 x 10^-15 m
To determine the de Broglie wavelength of a proton traveling at a given speed, we can use the de Broglie wavelength equation:
λ = h / mv
Where:
λ is the de Broglie wavelength,
h is the Planck's constant (h = 6.63 x 10^-34 J.s),
m is the mass of the particle,
and v is the speed of the particle.
Given:
v = 7.2 x 10^7 m/s
m = 1.67 x 10^-27 kg
Now, we can substitute the given values into the equation:
λ = (6.63 x 10^-34 J.s) / (1.67 x 10^-27 kg) x (7.2 x 10^7 m/s)
Simplifying the equation, we get:
λ = 3.95 x 10^-12 m
Therefore, the de Broglie wavelength of a proton traveling at the same speed as the electrons in a TV picture tube would be approximately 3.95 x 10^-12 meters.