Question

For particles having same K.E., the de-Broglie wavelength is

• A. Directly proportional to its velocity
• B. Inversely proportional to its velocity
• C. Independent of its mass and velocity
• D. Unpredictable

Answer 1

Answer: (A)

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{m_2{v}_2}{m_1{v}_1}$
$\frac{\frac{1}{2}{m}_2{v}_2^2}{\frac{1}{2}{m}_1{v}_1^2}\cdot \frac{v_1}{v_2}$
$=\frac{K.E_1}{K.E_2}=\frac{v_1}{v_2}$
As $K.E_1=K.E_2$
$\therefore \frac{{\lambda }_1}{{\lambda }_2}=\frac{v_1}{v_2}$ or $\lambda \propto v$