Example 13 Find the ratio of de Broglie wavelengths of two particles with the same momenta but different charges (q_(1)=2q_(2))

To find the ratio of de Broglie wavelengths of two particles with the same momenta but different charges, we can use the de Broglie wavelength formula: where is the de Broglie wavelength, is Planck's constant, and is the momentum of the particle.Given that the momenta of the two particles are the same, we can denote the momentum as .For the first particle with charge , the de Broglie wavelength is: For the second particle with charge , the de Broglie wavelength is: Since , we can express in terms of : Now, we can find the ratio of the de Broglie wavelengths: Therefore, the ratio of the de Broglie wavelengths of the two particles with the same momenta but different charges is 1:1.