A steel ball of mass m is moving with a kinetic energy K. The de Broglie wavelength associated with the ball is

Explanation:

de Broglie Wavelength:

de Broglie suggested that every moving particle has an associated wavelength, called the de Broglie wavelength, which is given by the formula:

λ = h / p, where:

λ = de Broglie wavelength

h = Planck's constant (6.626 × 10⁻³⁴ J·s)

p = Momentum of the particle (kg·m/s)

The momentum p is related to the kinetic energy K by the relation:

p = √(2mK), where:

m = mass of the particle (kg)

K = kinetic energy (J)

Using the formula for de Broglie wavelength and substituting the momentum:

λ = h / p = h / √(2mK)

∴ The de Broglie wavelength associated with the ball is h / √(2mK), which corresponds to Option 3.