# Question #81c98

Feb 9, 2017

$\textsf{\lambda = 1.17 \times {10}^{- 25} \textcolor{w h i t e}{x} n m}$

#### Explanation:

You need to use the de Broglie expression to get an object's wavelength:

$\textsf{\lambda = \frac{h}{m v}}$

$\textsf{\lambda}$ is the wavelength

$\textsf{h}$ is the Planck Constant = $\textsf{6.63 \times {10}^{- 34} \textcolor{w h i t e}{x} J s}$

$\textsf{m}$ is the mass

$\textsf{v}$ is the velocity

You need to get everything into standard units.

$\textsf{1000 \textcolor{w h i t e}{x} \text{g"=1"kg}}$

$\therefore$$\textsf{m = 145 \textcolor{w h i t e}{x} \text{g} = \frac{145}{1000} k g = 0.145 \textcolor{w h i t e}{x} k g}$

$\textsf{60 s = 1 \text{min}}$

$\textsf{60 \min = 1 h r}$

$\therefore$$\textsf{1 h r = 60 \times 60 = 3600 s}$

$\textsf{1000 m = 1 k m}$

$\therefore$$\textsf{v = \frac{141 , 000}{3600} = 39.16 \textcolor{w h i t e}{x} \text{m/s}}$

Now put in the numbers:

$\textsf{\lambda = \frac{6.63 \times {10}^{- 34}}{0.145 \times 39.16} m}$

$\textsf{\lambda = 1.167 \times {10}^{- 34} \textcolor{w h i t e}{x} m}$

$\textsf{1 n m = {10}^{- 9} m}$

To convert m to nm we divide by $\textsf{{10}^{- 9} \Rightarrow}$

$\textsf{\lambda = \frac{1.167 \times {10}^{- 34}}{{10}^{- 9}} = 1.17 \times {10}^{- 25} \textcolor{w h i t e}{x} n m}$
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