Question

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

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Solution

## Step 1. Given data: The de-Broglie wavelength of $X$ = $1{A}^{0}$. Mass of $Y\left({m}_{Y}\right)$ = $25%$mass of $X$, ( $0.25{m}_{X}$)Velocity of $Y$ $\left({v}_{Y}\right)$ = $75%$mass of $X$, ( $0.75{v}_{X}$)Step 2. Formula used:De Broglie wavelength $\mathrm{Î»}=h}{mv}$, where $h=$plank's constant, $m,v$are mass and velocity respectively.Step 3. Calculations:${\mathrm{Î»}}_{X}=1{A}^{0}=\frac{h}{{m}_{X}.{v}_{X}}$Also, ${\mathrm{Î»}}_{Y}=\frac{h}{{m}_{Y}Ã—{v}_{Y}}=\frac{h}{\left(0.25{m}_{X}Ã—0.75{v}_{X}\right)}=5.33\frac{h}{{m}_{X}.{v}_{X}}$, ( By putting the values of ${m}_{Y},{v}_{Y}$ )Thus, ${\mathrm{Î»}}_{Y}=5.33{A}^{0}$, ( By putting the value of ${\mathrm{Î»}}_{X}$)Hence, de Broglie's wavelength of $Y$ will be $5.33{A}^{0}$.

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