To calculate the de Broglie wavelength for a particle, you can use the formula:
\[
\lambda = \frac{h}{p}
\]
Where:
- \(\lambda\) is the de Broglie wavelength
- \(h\) is the Planck's constant (6.626 x 10^-34 Js)
- \(p\) is the momentum of the particle
To find the momentum (\(p\)) of the particle, you can use the formula:
\[ p = m \times v \]
Where:
- \(m\) is the mass of the particle (2.2 x 10^-2 kg)
- \(v\) is the velocity of the particle (10 m/s)
1. Calculate the momentum of the particle:
\[
p = 2.2 \times 10^{-2} \, \text{kg} \times 10 \, \text{m/s}
\]
\[
p = 0.22 \, \text{kg} \cdot \text{m/s}
\]
2. Substitute the momentum value into the de Broglie wavelength formula:
\[
\lambda = \frac{6.626 \times 10^{-34} \, \text{J s}}{0.22 \, \text{kg} \cdot \text{m/s}}
\]
3. Calculate the de Broglie wavelength:
\[
\lambda = 3.012727 \times 10^{-33} \, \text{m}
\]
Therefore, the de Broglie wavelength for a particle with a mass of 2.2 x 10^-2 kg and a velocity of 10 m/s is approximately 3.012727 x 10^-33 meters.
