Question

The wavelength of the de Broglie wave (in meter) associated with a particle of mass \(m\) moving with \(\frac{1}{10}\) of the velocity of light is (h = Planck's constant, c = velocity of light):

• A. \(\frac{5h}{mc}\)
• B. \(\frac{h}{mc}\)
• C. \(\frac{10h}{mc}\)
• D. \(\frac{2h}{mc}\)
• E. \(\frac{4h}{mc}\)

Hint:

The de Broglie wavelength relates the wave properties of a particle to its momentum, where the momentum is the product of mass and velocity.

Answer 1

The Correct Option is C

The de Broglie wavelength \( \lambda \) is given by: \[ \lambda = \frac{h}{p} \] where \( p \) is the momentum of the particle. The momentum \( p = mv \), and for a particle moving at \(\frac{1}{10}\) of the velocity of light: \[ v = \frac{c}{10} \] Thus, the momentum is: \[ p = m \times \frac{c}{10} = \frac{mc}{10} \] Substituting this into the de Broglie formula: \[ \lambda = \frac{h}{\frac{mc}{10}} = \frac{10h}{mc} \]