Question

A particle X moving with a certain velocity has a de-Broglie wavelength of $1A^0$. If particle Y has a mass of 25 % that of X and velocity $75\%$ that of X, de Broglie's wavelength of Y will be:

• A. $3A^o$
• B. $5.33A^o$
• C. $6.880A^o$
• D. $48A^o$

Answer 1

The correct option is B $5.33A^o$

According to question,

$m_Y=m_X\times \frac{25}{100}=0.25m_X$

and $v_Y=v_X\times \frac{75}{100}=0.75v_X$

De brogile wavelength $\lambda =\frac{h}{mv}$

${\lambda }_X=1A^0=\frac{h}{m_X\times v_X}$

${\lambda }_Y=\frac{h}{(0.25m_X\times 0.75v_X)}=5.33\frac{h}{m_X\times v_X}=5.33A^0$