Question 197: Dual Nature of Matter and Radiation

Question

A particle 'P' is formed due to a completely
inelastic collision of particles 'x' and 'y' having
de-Broglie wavelengths '$$\lambda $$x' and '$$\lambda $$y'
respectively. If x and y were moving in opposite
directions, then the de-Broglie wavelength of
'P' is :-

Accepted Answer

Conservation of momentum
$$\overrightarrow {{p_x}}  + \overrightarrow {{p_y}}  = {\overrightarrow p _{final}}$$
m
x
v
x
Ã¢ÂÂ m
y
v
y
= (m
x
+ m
y
) V
$${h \over {{\lambda _x}}} - {h \over {{\lambda _y}}} = {h \over \lambda }$$
$$ \Rightarrow \lambda  = {{{\lambda _x}{\lambda _y}} \over {\left| {{\lambda _x} - {\lambda _y}} \right|}}$$

Answer

$${\lambda _x} - {\lambda _y}$$

Answer

$${{{\lambda _x}{\lambda _y}} \over {\left| {{\lambda _x} - {\lambda _y}} \right|}}$$

Answer

$${\lambda _x} + {\lambda _y}$$

Answer

$${{{\lambda _x}{\lambda _y}} \over {{\lambda _x} + {\lambda _y}}}$$

Dual Nature of Matter and Radiation

A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '$\lambda x' and '\lambda $y' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

Choose the correct answer: