Question

If an object moves with a velocity of 1 km/s and has a mass of 0.033 kg, calculate the de Broglie wavelength of the object.

• A. \( 1.7 \times 10^{-35} \, \text{m} \)
• B. \( 1.1 \times 10^{-32} \, \text{m} \)
• C. \( 2 \times 10^{-35} \, \text{m} \)
• D. \( 3 \times 10^{-25} \, \text{m} \)

Hint:

For calculating the de Broglie wavelength of a particle, use \( \lambda = \frac{h}{mv} \), where \( h \) is Planck's constant, \( m \) is the mass of the object, and \( v \) is its velocity.

Answer 1

The Correct Option is C

Step 1: Using the de Broglie wavelength formula.
The de Broglie wavelength \( \lambda \) is given by: \[ \lambda = \frac{h}{mv} \] where: - \( h = 6.63 \times 10^{-34} \, \text{Js} \) (Planck's constant), - \( m = 0.033 \, \text{kg} \) (mass of the object), - \( v = 1 \, \text{km/s} = 1000 \, \text{m/s} \) (velocity of the object).
Step 2: Substituting values into the formula.
Substitute the given values into the formula: \[ \lambda = \frac{6.63 \times 10^{-34}}{0.033 \times 1000} = 2 \times 10^{-35} \, \text{m} \]
Step 3: Conclusion.
The de Broglie wavelength is \( 2 \times 10^{-35} \, \text{m} \), so the correct answer is (C).