If a proton were traveling the same speed as electrons in a TV picture tube (about 7.8 107 m/s), what would its de Broglie wavelength be? The mass of a proton is 1.67 10-27 kg.
To find the de Broglie wavelength of a proton, we can use the de Broglie equation:
λ = h / p
Where:
λ is the de Broglie wavelength,
h is the Planck's constant (h = 6.626 x 10^(-34) J·s),
p is the momentum of the proton.
To calculate the momentum of the proton, we can use the equation:
p = mv
Where:
m is the mass of the proton,
v is the velocity of the proton.
Given:
Mass of a proton, m = 1.67 x 10^(-27) kg
Velocity of electrons in the TV picture tube, v = 7.8 x 10^7 m/s
First, calculate the momentum of the proton.
p = (1.67 x 10^(-27) kg) * (7.8 x 10^7 m/s)
Now, find the de Broglie wavelength using the de Broglie equation.
λ = (6.626 x 10^(-34) J·s) / (momentum of the proton)
By plugging in the calculated momentum value into the equation, we can determine the de Broglie wavelength of the proton.