Calculate the wavelength of a proton with energy 2.45 eV.

2.45eV = 3.92E-19 J

Then E = hc/wavelength. Solve for wavelength.

To calculate the wavelength of a proton with a given energy, we can 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 or 4.136 x 10^-15 eV·s)
p is the momentum of the proton, which can be calculated using the equation:

p = √(2mE)

Where:
m is the mass of the proton (1.67 x 10^-27 kg)
E is the energy of the proton (in joules)

First, we need to convert the energy of the proton from eV to joules by multiplying by the conversion factor: 1 eV = 1.602 x 10^-19 J.

So, for the given energy of 2.45 eV:
E = 2.45 eV x 1.602 x 10^-19 J/eV = 3.92 x 10^-19 J

Next, we can calculate the momentum of the proton using the equation:

p = √(2mE)

p = √(2 x 1.67 x 10^-27 kg x 3.92 x 10^-19 J)

p = √(13.12 x 10^-46 kg·J)

p = 3.62 x 10^-23 kg·m/s

Now, we can use the de Broglie wavelength equation to calculate the wavelength:

λ = h / p

λ = (6.626 x 10^-34 J·s) / (3.62 x 10^-23 kg·m/s)

λ = 1.83 x 10^-11 meters

So, the wavelength of the proton with an energy of 2.45 eV is approximately 1.83 x 10^-11 meters.