Question

if the kinetic energy of a free electron double its deBroglie wavelength change by the factor is

Answer 1

Ans : (c)

λ=hmvandK=12mv2=(mv)22mλ=hmvandK=12mv2=(mv)22m

⇒mv=2mK−−−−√⇒mv=2mK

So, λ=h2mK−−−−−√λ=h2mK

⇒λ∼1K−−√⇒λ∼1K

λ2λ1=K1−−−√K2−−−√=K1−−−√2K1−−−−√(K2=2K1)λ2λ1=K1K2=K12K1(K2=2K1)

⇒λ2λ1=12–√

Answer 2

Hey there! Your answer is 1/root2 which is the change.
You can use the formula lamda=h/root over of 2mk