Question

# Suppose that photons of blue light (430 nm) are used to locate the position of a 2.80-g Ping Pong ball in flight and that the uncertainty in the position is equal to one wavelength. What is the minimum uncertainty in the speed of the Ping-Pong ball? Comment on the magnitude of your result.

Solution

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Determine the value of the mass in SI units:

1. Begin with the mass in grams.

2. Use a conversion factor to convert grams into kilograms.

\begin{align*} m&= \begin{array}{c|c} 2.80\;\cancel{\mathrm{g}}& 1\;\mathrm{kg}\\ \hline & 1000\;\cancel{\mathrm{g}} \end{array}\\ &=2.80\times10^{-3}\;\mathrm{kg} \end{align*}

Determine the value of the minimum uncertainty of the position in SI units:

1. Begin with the minimum uncertainty of the position in nanometers.

2. Use a conversion factor to convert nanometers into meters.

\begin{align*} \Delta x&= \begin{array}{c|c} 430\;\cancel{\mathrm{nm}}& 10^{-9}\;\mathrm{m}\\ \hline & 1\;\cancel{\mathrm{nm}} \end{array}\\ &= 4.30\times10^{-7}\;\mathrm{m} \end{align*}

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