Effective wavelength is a concept used in quantum mechanics to describe the wave-like behavior of particles, such as protons. It is calculated by dividing the momentum of the particle by its mass, and then taking the reciprocal of the result.



To calculate the accelerating potential required to give a proton an effective wavelength of 0.005nm, we first need to calculate the momentum of the proton. We can use the de Broglie equation to do this, which states that the momentum of a particle is equal to its wavelength multiplied by Planck's constant.







Now that we have calculated the momentum of the proton, we can use the formula for the kinetic energy of a particle to calculate the accelerating potential required. The formula is:

























In conclusion, the accelerating potential required to give a proton an effective wavelength of 0.005nm is approximately 58,540 volts. This value was calculated by first finding the momentum of the proton using the de Broglie equation and then using the formula for kinetic energy to calculate the accelerating potential required.

E = 1240/wavelength (nm) eV
= 1240/0.005 eV
=248000 eV

now, electrostatic energy = energy of proton
or, charge of proton × potential = 248000eV
or, e × potential = 248000 eV
or, potential = 248000V