Calculate the wavelength of de Broglie waves associated with a proton having $\displaystyle \left(\frac{500}{1 \cdot 673}\right)$ eV energy. How will the wavelength be affected for an alpha particle having the same energy ?

Effect on wavelength \[\lambda=\frac{h}{\sqrt{2 m K}} \] \(\displaystyle K=\left(\frac{500}{1.673}\right) e V\) \[=\frac{500 \times 1.6 \times 10^{-19}}{1.673} J \] \[\lambda_{p}=\frac{6.63 \times 10^{-34}}{\sqrt{2 \times 1.673 \times 10^{-27} \times\left(\dfrac{500 \times 1.6 \times 10^{-19}}{1.673}\right)}} \] \[=1.65 \times 10^{-12} \mathrm{~m} \] \[\lambda \alpha \frac{1}{\sqrt{m}} \]