Question

The wavelength associated with a golf ball weighing $200g$ and moving with a speed of $5m/h$ is of the order of:

• A. ${10}^{-10}m$
• B. ${10}^{-20}m$
• C. ${10}^{-30}m$
• D. ${10}^{-40}m$

Answer 1

The correct option is C ${10}^{-30}m$

$Explanation:$

$FromDeBroglieTheoremforwavelength:$

$\lambda =\frac{h}{mv}\to \left(1\right)$

$where,$

$\lambda =Wavelength$

$h=Planc{k}^{\prime }sconstant=6.625\times {10}^{-34}$

$m=massoftheelement=200gm=200\times {10}^{-3}Kg=0.2Kg$

$V=Velocity=5m/h=\frac{5}{3600}m/s=\frac{5}{3.6}\times {10}^{-3}m/s=1.39\times {10}^{-3}m/s$

$Substituteallvaluesinequation1weget:$

$\lambda =\frac{6.625\times {10}^{-34}}{0.2\times 1.39\times {10}^{-3}}=2.38\times {10}^{-30}$

$\therefore \lambda =2.38\times {10}^{-30}$

$Herearegettingvalueintermsof{10}^{-30}$

$Hencecorrectanswerisoption\left(A\right)$