Calculate the wavelength of a proton with energy 2.45 eV.
E = hc/wavelength
2.45 eV = 3.92E-19 J; substitute for E.
h = Planck's constant
c = speed of light.
Substitute and solve for wavelength in meters.
To calculate the wavelength of a proton, you need to use the de Broglie wavelength equation:
λ = h / p
where λ is the wavelength, h is the Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the proton.
To find the momentum of the proton, you can use the equation:
p = √(2mE)
where p is the momentum, m is the mass of the proton (1.67 x 10^-27 kg), and E is the energy of the proton.
Given that the energy of the proton is 2.45 eV, we need to convert it to joules:
1 eV = 1.602 x 10^-19 J
Therefore, 2.45 eV = 2.45 x 1.602 x 10^-19 J = 3.9249 x 10^-19 J.
Now, we can calculate the momentum:
p = √(2 * 1.67 x 10^-27 kg * 3.9249 x 10^-19 J)
p = √(1.3084 x 10^-46 kg·J)
p = 1.1436 x 10^-23 kg·m/s
Finally, we can substitute the momentum into the de Broglie wavelength equation to find the wavelength:
λ = 6.626 x 10^-34 J·s / (1.1436 x 10^-23 kg·m/s)
λ = 5.788 x 10^-12 meters
Therefore, the wavelength of a proton with an energy of 2.45 eV is approximately 5.788 x 10^-12 meters.