Question

a certain rifle bullet has a mass of 7.41 g. calculate the de broglie wavelength of the bullet traveling at 1073 mile per hour.
round and report your answer to 3 significant figures.
short answer
type answer here

Explanation:

Step1: Convert units

• Convert mass from grams to kilograms: \(m = 7.41\space g=7.41\times10^{- 3}\space kg\)
• Convert speed from miles per hour to meters per second.

We know that \(1\space mile = 1609.34\space m\) and \(1\space hour=3600\space s\).
\(v = 1073\space\frac{mile}{hour}\times\frac{1609.34\space m}{1\space mile}\times\frac{1\space hour}{3600\space s}\approx479.7\space m/s\)

Step2: Use de - Broglie formula

The de - Broglie formula is \(\lambda=\frac{h}{mv}\), where \(h = 6.626\times10^{-34}\space J\cdot s\) (Planck's constant), \(m\) is the mass of the object, and \(v\) is the velocity of the object.
Substitute \(h = 6.626\times10^{-34}\space J\cdot s\), \(m = 7.41\times 10^{-3}\space kg\), and \(v\approx479.7\space m/s\) into the formula:
\(\lambda=\frac{6.626\times10^{-34}}{7.41\times10^{-3}\times479.7}\)
\(\lambda=\frac{6.626\times10^{-34}}{3.554\times10^{0}}\)
\(\lambda\approx1.86\times10^{-34}\space m\)

Answer:

\(1.86\times 10^{-34}\space m\)