The de Broglie wavelength ($\lambda$) of an object is given by the formula:

$\lambda = \frac{h}{mv}$

where:

• $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{Js}$)
• $m$ is the mass of the object (in kilograms, kg)
• $v$ is the velocity of the object (in meters per second, m/s)

Given:

• $m = 20.9 \, \text{kg}$
• $v = 634 \, \text{m/s}$

Now, calculate the de Broglie wavelength:

$\lambda = \frac{6.626 \times 10^{-34} \, \text{Js}}{20.9 \, \text{kg} \times 634 \, \text{m/s}}$

First, calculate the denominator:

$20.9 \times 634 = 13262.6 \, \text{kg} \cdot \text{m/s}$

Now, compute the de Broglie wavelength:

$\lambda = \frac{6.626 \times 10^{-34}}{13262.6}$

$\lambda \approx 4.996 \times 10^{-38} \, \text{m}$

Rounding to three significant figures:

$\lambda \approx 5.00 \times 10^{-38} \, \text{m}$

Therefore, the de Broglie wavelength of the shell is:

$\boxed{5.00 \times 10^{-38} \, \text{m}}$

Would you like more details or have any questions? Here are some related questions for further exploration:

1. What is the significance of the de Broglie wavelength in quantum mechanics?
2. How does the de Broglie wavelength change with velocity?
3. Can the de Broglie wavelength be measured for macroscopic objects?
4. What is Planck's constant, and why is it important?
5. How does the de Broglie wavelength relate to the concept of wave-particle duality?
6. What is the formula for kinetic energy in classical mechanics?
7. How is the de Broglie wavelength relevant to electron microscopy?
8. What are some practical applications of de Broglie wavelengths in technology?

Tip: The de Broglie wavelength is generally significant for microscopic particles like electrons. For macroscopic objects, the wavelength becomes extremely small and usually negligible in practice.