Example 14 Find the De Broglie wavelength dr electron that moves at a speed of 2,2cdot 10^6m/s is (m) (h=6,6210^34Js,m_(e)=9,1cdot 10^-31kg)

To find the De Broglie wavelength of an electron moving at a speed of $2.2 \times 10^6 \, \text{m/s}$, we can use the De Broglie equation:<br /><br />\[ \lambda = \frac{h}{mv} \]<br /><br />where:<br />- \( \lambda \) is the De Broglie wavelength,<br />- \( h \) is Planck's constant (\(6.62 \times 10^{-34} \, \text{Js}\)),<br />- \( m \) is the mass of the electron (\(9.1 \times 10^{-31} \, \text{kg}\)),<br />- \( v \) is the speed of the electron (\(2.2 \times 10^6 \, \text{m/s}\)).<br /><br />Now, plug in the values:<br /><br />\[ \lambda = \frac{6.62 \times 10^{-34}}{(9.1 \times 10^{-31}) \times (2.2 \times 10^6)} \]<br /><br />\[ \lambda = \frac{6.62 \times 10^{-34}}{1.992 \times 10^{-24}} \]<br /><br />\[ \lambda \approx 3.34 \times 10^{-10} \, \text{m} \]<br /><br />So, the De Broglie wavelength of the electron is approximately \(3.34 \times 10^{-10} \, \text{m}\).