The de-Broglie wavelength associated with a ball of mass 1 kg having kinetic energy 0.5 J is

The de-Broglie wavelength (λ) is given by the equation:

λ = h / p

where h is Planck's constant (6.626 x 10^-34 Js) and p is the momentum of the particle.

The momentum (p) of a particle can be found from its kinetic energy (K.E) using the equation:

K.E = p² / 2m

where m is the mass of the particle.

Rearranging for p gives:

p = sqrt(2mK.E)

Substituting the given values:

p = sqrt(2 * 1 kg * 0.5 J) = sqrt(1 kg m²/s²) = 1 kg m/s

Substituting this into the equation for λ gives:

λ = h / p = 6.626 x 10^-34 Js / 1 kg m/s = 6.626 x 10^-34 m

So, the de-Broglie wavelength associated with a ball of mass 1 kg having kinetic energy 0.5 J is 6.626 x 10^-34 m.