Question

A sub-atomic particle of mass \( 10^{-30} \) kg is moving with a velocity of \( 2.21 \times 10^6 \) m/s. Under the matter wave consideration, the particle will behave closely like            (h = \( 6.63 \times 10^{-34} \) J.s)

• A. Infra-red radiation
• B. X-rays
• C. Gamma rays
• D. Visible radiation

Hint:

The de Broglie wavelength can be used to calculate the behavior of particles as waves. If the wavelength is on the order of \( 10^{-10} \) m, the particle behaves like X-rays.

Answer 1

The Correct Option is B

The de Broglie wavelength \( \lambda \) of a particle is given by the formula: \[ \lambda = \frac{h}{p}, \] where: - \( h = 6.63 \times 10^{-34} \) J.s is Planck's constant, - \( p = mv \) is the momentum of the particle, - \( m = 10^{-30} \) kg is the mass of the particle, - \( v = 2.21 \times 10^6 \) m/s is the velocity of the particle. Substitute the values into the formula: \[ \lambda = \frac{6.63 \times 10^{-34}}{(10^{-30}) \times (2.21 \times 10^6)} = \frac{6.63 \times 10^{-34}}{2.21 \times 10^{-24}} = 3 \times 10^{-10} \text{ m}. \] This wavelength is in the range of X-rays. Thus, the correct answer is: \[ \boxed{2}. \]