Given, initial kinetic energy,
E1=E Initial de-Broglie wavelength,
λ1=λ Consider the wavelength of particle changes to
75% of λ after
providing energy ∆E to the particle.
Hence, final wavelength of particle,
λ2=0.75λ Final energy,
E2=E+ΔE Relationship between de-Broglie wavelength and energy of particleis given as
λ= Here, h is Planck’s constant and m is mass of particle which is alsoconstant term.
Therefore, we get
λ∝ Thus, we can write the relationship as
= ⇒= ⇒= Squaring both sides of above equation, we get
⇒= ⇒16E=9E+9ΔE ΔE=E