Question

The de-Broglie wavelength of a particle with mass 1 g and velocity 100 m/s is

• A. $6.63 \times 10^{-33} m$
• B. $6.63 \times 10^{-34} m$
• C. $6.63 \times 10^{-35} m$
• D. $6.63 \times 10^{-36} m$

Answer 1

The Correct Option is A

The de Broglie wavelength is a fundamental concept that relates the momentum of a particle to its wavelength. The formula for calculating the de Broglie wavelength \(\lambda\) is:

\(\lambda = \frac{h}{mv}\)

where:

• \(h\) is Planck's constant, approximately \(6.63 \times 10^{-34} \, \text{Js}\).
• \(m\) is the mass of the particle.
• \(v\) is the velocity of the particle.

Given:

• Mass \(m = 1 \, \text{g} = 0.001 \, \text{kg}\) (since 1 g = 0.001 kg).
• Velocity \(v = 100 \, \text{m/s}\).
• Planck's constant \(h = 6.63 \times 10^{-34} \, \text{Js}\).

Substitute these values into the de Broglie wavelength formula:

\(\lambda = \frac{6.63 \times 10^{-34}}{0.001 \times 100}\)

\(\lambda = \frac{6.63 \times 10^{-34}}{0.1}\)

\(\lambda = 6.63 \times 10^{-33} \, \text{m}\)

Thus, the de Broglie wavelength of the particle is \(6.63 \times 10^{-33} \, \text{m}\), which corresponds to the correct option.

Therefore, the correct answer is: \(6.63 \times 10^{-33} \, \text{m}\).