Question

Calculate the de Broglie wavelength associated with an $\alpha$-particle having an energy of $7.7\times {10}^{-13}J$ and a mass of $6.6\times {10}^{-24}g$. $(h=6.6\times {10}^{-34}J-s)$.

• A. $6.56\times {10}^{-10}cm$.
• B. $6.56\times {10}^{-15}dm$.
• C. $6.56\times {10}^{-12}cm$.
• D. $6.56\times {10}^{-14}dm$.

Answer 1

The correct option is D $6.56\times {10}^{-14}dm$.

$\lambda =\frac{h}{mv}$ $\dots$[de-broglie wave length]

$\because E=\frac{1}{2}m{v}^2⟹mv=\sqrt{2mE}$

$\therefore \lambda =\frac{h}{\sqrt{2mE}}=\frac{6.6\times {10}^{-23}}{\sqrt{2\times 6.6\times {10}^{-27}\times 7.7\times {10}^{-13}J}}=6.56\times {10}^{-14}dm$