Question

A particle $X$ moving with a certain velocity has a de Broglie wavelength of $1\mathring{A}.$ If particle $Y$ has a mass of $25\%$ that of $X$ and velocity $75\%$ that of $X$, then de Broglie's wavelength of $Y$ will be:

• A. $3\mathring{A}$
• B. $5.33\mathring{A}$
• C. $6.88\mathring{A}$
• D. $48\mathring{A}$

Answer 1

Answer: (B)

$5.33\mathring{A}$

$\frac{{\lambda }_x}{{\lambda }_y}=\frac{m_y\times v_y}{m_x\times v_x}$

$\frac{1}{{\lambda }_y}=\frac{\frac{25}{100}{m}_x.\frac{75}{100}{v}_x}{m_x{v}_x}$

$\Rightarrow {\lambda }_y=\frac{16}{3}=5.33A^0$

Hence, the correct option is $B$