Calculate the wavelength of a proton with energy 2.45 eV.
Enter the numerical value in m
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To calculate the wavelength of a proton with a given energy, you can use the 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 (p) of the proton, you can use the equation:
p = √(2mE)
where m is the mass of the proton (1.67 x 10^-27 kg) and E is the energy (2.45 eV).
First, convert the energy from electron volts (eV) to joules (J):
1 eV = 1.6 x 10^-19 J
So, 2.45 eV = 2.45 x 1.6 x 10^-19 J = 3.92 x 10^-19 J
Now, substitute the values into the equation for momentum:
p = √(2 * 1.67 x 10^-27 kg * 3.92 x 10^-19 J)
p ≈ 4.69 x 10^-24 kg⋅m/s
Finally, substitute the momentum into the equation for the wavelength:
λ = 6.626 x 10^-34 J⋅s / 4.69 x 10^-24 kg⋅m/s
λ ≈ 1.41 x 10^-10 meters
Therefore, the wavelength of the proton with an energy of 2.45 eV is approximately 1.41 x 10^-10 meters (m).