Question

The de Broglie wavelength associated with a steel ball of mass 100 g moving at a speed of 1 m/s is:

• A. \( 6.62 \times 10^{-34} \) m
• B. \( 6.62 \times 10^{-37} \) m
• C. \( 6.62 \times 10^{-39} \) m
• D. \( 6.62 \times 10^{-30} \) m

Hint:

The de Broglie wavelength is used to describe the wave-like behavior of particles, and it depends on the particle's mass and velocity.

Answer 1

The Correct Option is C

Step 1: Use de Broglie wavelength relation
The de Broglie wavelength of a moving particle is given by:
\( \lambda = \frac{h}{mv} \)

Where, \( h = 6.62 \times 10^{-34}\ \text{J s} \), \( m = 0.1\ \text{kg} \), \( v = 1\ \text{m/s} \)

Step 2: Substitute values
\[ \lambda = \frac{6.62 \times 10^{-34}}{0.1 \times 1} \] \[ \lambda = 6.62 \times 10^{-33}\ \text{m} \]

Final Answer:
\( \lambda = 6.62 \times 10^{-33}\ \text{m} \)