Question

Two fast moving particles $X$ and $Y$ are associated with de Broglie wavelengths $1$nm and $4$ nm respectively. If mass of $X$ in nine times the mass of $Y$, the ratio of kinetic energies of $X$ and $Y$ would be:

• A. $3:1$
• B. $9:1$
• C. $5:12$
• D. $16:9$

Answer 1

The correct option is D $16:9$

$\lambda =h/mv$

$\frac{{\lambda }_2}{{\lambda }_1}=\frac{m_1{v}_1}{m_2{v}_2}=\frac{4}{1}=\frac{9\times v_2}{1\times v_1}$

$\frac{v_2}{{}_1}=\frac{9}{4}$

$K.E=12m{v}^2$

Ratio of K.E = $\frac{K.E_1}{K.E_2}=16:9$