Question

If the mass of a microscopic particle a well as its speed are halved, the de-broglie wavelength associated with the particle will

• A. increased by a factor more than $2$
• B. increases by a factor of $2$
• C. decreases by a factor of $2$
• D. decrease by a factor more than $2$

Answer 1

The correct option is A increased by a factor more than $2$

$\lambda$ is directly proportional to $\frac{1}{mv}$

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{m_2{v}_2}{m_1{v}_1}$

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{1}{2}\times \frac{1}{2}$

${\lambda }_2=4{\lambda }_1$