Question

At what velocity ratio $\frac{v_e}{v_p}$ are the wavelengths of an electron and a proton equal?
$(m_e=9.1\times {10}^{-28}gand{m}_p=1.6725\times {10}^{-24}g)$.

• A. $1.2\times {10}^3$.
• B. $1.8\times {10}^3$.
• C. $2.4\times {10}^3$.
• D. $1.6\times {10}^3$.

Answer 1

The correct option is B $1.8\times {10}^3$.

$\lambda =\frac{h}{mv}$

${\lambda }_e=\frac{h}{m_e{v}_e}$ and ${\lambda }_p=\frac{h}{m_p{v}_p}$

${\lambda }_e={\lambda }_p⟹\frac{v_3}{v_p}=\frac{m_p}{m_e}=\frac{1.6725\times {10}^{-23}}{9.1\times {10}^{-28}}=1.8\times {10}^3$