Question

Two particles A and B are in motion . If the wavelength associated with particle A is $5\times {10}^{-8}m$. Calculate the wavelength associated with particle B if its momentum is half of A.

• A. $5\times {10}^{-8}m$
• B. ${10}^{-5}cm$
• C. ${10}^{-6}cm$
• D. $5\times {10}^{-8}cm$

Answer 1

Answer: (C)

${10}^{-6}cm$

$(mv{)}_A=\frac{h}{{\lambda }_A}$

$(mv{)}_B=\frac{h}{{\lambda }_B}$

$(mv{)}_B=\frac{1}{2}(mv{)}_A$

$\frac{h}{{\lambda }_B}=\frac{h}{2{\lambda }_A}$

$2\times 5\times {10}^{-8}$ m

=$10\times {10}^{-8}$

=${10}^{-7}m={10}^{-6}cm$

Hence, the correct option is $C$