Answer to Question #132235 in Mechanics | Relativity for Max

Question

What is ratio of De-broglie wavelegth of proton and electron at same kinetic energy.

Answer 1

solution:-

de-broglie wavelength can be written as

$\lambda=\frac{h}{p}=\frac{h}{mv}=\frac{h}{\sqrt{2mKE}}$

therefore de-broglie wavelength for proton

$\lambda _p=\frac{h}{\sqrt{2m_pKE_p}}...........eq.1$

de-brolie wavelength for electron can written as

$\lambda _e=\frac{h}{\sqrt{2m_eKE_e}}...........eq.2$

from equation 1 and 2 we can write

$\frac{\lambda _p}{\lambda _e}=\sqrt{\frac{m_e}{m_p}}$

because kinetic energy is same for proton and electron

$\frac{\lambda _p}{\lambda _e}=\sqrt{\frac{9.1\times10^{-31}}{1.67\times10^{-27}}}=\frac{0.02}{1}$

therefore ratio of de-broglie waelength of proton and electron is 0.02:1