Question

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

• A. $3$
• B. $5.33$
• C. $6.88$
• D. $48$

Answer 1

The correct option is B $5.33$

We know,

$\frac{{\lambda }_y}{{\lambda }_x}=\frac{m_x{V}_x}{m_y{V}_y}$

$\Rightarrow \frac{{\lambda }_y}{1}=\frac{m_x{V}_x}{\left(0.25m_x\right)\left(0.75V_x\right)}=\frac{16}{3}$

$\therefore {\lambda }_y=5.33nm$