Question

Calculate the ratio of de broglie wavelength associated with a deutron moving with velocity 2v and alpha particle moving with velocity v

Answer 1

Given velocity of deutron = 2v and

velocity of alpha particle = v

Mass of  deutron =3.343 ×10⁻²⁷ kg

Mass of alpha particle = 6.644 ×10⁻²⁷ kg

Now we know De Brogile wavelength is expressed mathematically as

λ = h/p ------(A)

where h = planks constant and

p=momentum = mass × velocity

Now reducing the given values and above formula in (A) we get,

For duetron

λ₁ = h/(3.343 ×10⁻²⁷ × 2v) ------(1)

For alpha particle

λ₂ = h/(6.644 ×10⁻²⁷ × v) ------(2)

Now dividing 1 by 2 we get,

λ₁/λ₂ = {h/(3.343 ×10⁻²⁷ × 2v)}/h/{(6.644 ×10⁻²⁷ × v)}

λ₁/λ₂ = 6.644/6.684 ≈ 1