Question

What is the de Broglie wavelength corresponding to a ball of mass 100 g moving with a speed of 33 m/s? (Plank's constant-6.6 x10^-34 J/s)

• A. 1x10^-34 m
• B. 2x10^-34 m
• C. 3x10^-34 m
• D. 1x10³⁴ m
• E. 2x10³⁴ m

Answer 1

The Correct Option is B

Given:

• Mass of the ball, \( m = 100 \, \text{g} = 0.1 \, \text{kg} \)
• Speed of the ball, \( v = 33 \, \text{m/s} \)
• Planck's constant, \( h = 6.6 \times 10^{-34} \, \text{J} \cdot \text{s} \)

Step 1: De Broglie Wavelength Formula

The de Broglie wavelength (\( \lambda \)) is given by:

\[ \lambda = \frac{h}{p} = \frac{h}{m v} \]

where \( p \) is the momentum of the object.

Step 2: Substitute the Given Values

\[ \lambda = \frac{6.6 \times 10^{-34}}{0.1 \times 33} \]

\[ \lambda = \frac{6.6 \times 10^{-34}}{3.3} \]

\[ \lambda = 2 \times 10^{-34} \, \text{m} \]

Conclusion:

The de Broglie wavelength corresponding to the ball is \( 2 \times 10^{-34} \, \text{m} \).

Answer: \(\boxed{B}\)

Answer 2

Step 1: Recall the formula for de Broglie wavelength.

The de Broglie wavelength (\( \lambda \)) of a particle is given by:

\[ \lambda = \frac{h}{p}, \]

where:

• \( h \) is Planck's constant ( \(h = 6.6 \times 10^{-34} \, \text{J.s}\)),
• \( p \) is the momentum of the particle, given by \( p = mv \),
• \( m \) is the mass of the particle, and
• \( v \) is the velocity of the particle.

 

We are given:

• \( m = 100 \, \text{g} = 0.1 \, \text{kg}, \)
• \( v = 33 \, \text{m/s}, \)
• \( h = 6.6 \times 10^{-34} \, \text{Js}. \)

 

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Step 2: Calculate the momentum (\( p \)).

The momentum of the ball is:

\[ p = mv = 0.1 \times 33 = 3.3 \, \text{kgm/s}. \]

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Step 3: Substitute into the de Broglie wavelength formula.

Substitute \( h = 6.6 \times 10^{-34} \, \text{J·s} \) and \( p = 3.3 \, \text{kgm/s} \):

\[ \lambda = \frac{h}{p} = \frac{6.6 \times 10^{-34}}{3.3}. \]

Simplify:

\[ \lambda = 2 \times 10^{-34} \, \text{m}. \] ---

Final Answer: The de Broglie wavelength is \( \mathbf{2 \times 10^{-34} \, \text{m}} \), which corresponds to option \( \mathbf{(B)} \).