Question

The de broglie wavelength of particles of kinetic energy k is lambda what would be the wavelength of the particle if its kinetic energy were k/4

Answer 1

Using the de-broglie Relation,

λ = h/mv

now, K = 1/2 mv²

∴ v = √(2K/m)

∴ λ = h/m×√(2K/m)

∴  λ = h/√(2mK)

This is the Relation which we will use to determine the required result in question.

When Kinetic energy is K, and Wavelength is λ, then,

λ = h/√2mK

Now, When Kinetic energy is k/4 then

λ = h/(√2m × k/4)

∴ λ = h/(√mk/2)

Hope it helps .

Answer 2

Using the de-broglie Relation,

λ = h/mv

now, K = 1/2 mv²

∴ v = √(2K/m)

∴ λ = h/m×√(2K/m)

∴  λ = h/√(2mK)

This is the Relation which we will use to determine the required result in question.

When Kinetic energy is K, and Wavelength is λ, then,

λ = h/√2mK

Now, When Kinetic energy is k/4 then

λ = h/(√2m × k/4)

∴ λ = h/(√mk/2)