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(A) According to the de Broglie equation,$\lambda = h / p$,where $\lambda$ is the wavelength,$h$ is Planck's constant,and $p$ is the momentum.Given $\

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$1000 \ \mathring{A}$

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(A) According to the de Broglie equation,$\lambda = h / p$,where $\lambda$ is the wavelength,$h$ is Planck's constant,and $p$ is the momentum.Given $\lambda_{A} = 5 	imes 10^{-8} \ m$ and $p_{B} = 0.5 \ p_{A}$.Since $\lambda \propto 1 / p$,we have $\lambda_{B} / \lambda_{A} = p_{A} / p_{B}$.Substituting $p_{B} = 0.5 \ p_{A}$,we get $\lambda_{B} / \lambda_{A} = p_{A} / (0.5 \ p_{A}) = 2$.Therefore,$\lambda_{B} = 2 	imes \lambda_{A} = 2 	imes 5 	imes 10^{-8} \ m = 10^{-7} \ m$.Converting to $\mathring{A}$: $1 \ m = 10^{10} \ \mathring{A}$,so $10^{-7} \ m = 10^{-7} 	imes 10^{10} \ \mathring{A} = 1000 \ \mathring{A}$.

Two particles $A$ and $B$ are in motion. If the wavelength associated with particle $A$ is $5 \times 10^{-8} \ m$,calculate the wavelength (in $\mathring{A}$) associated with particle $B$ if its momentum is half of $A$.

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