Question

What will happen to the wavelength associated with a moving particle of its velocity is doubled?

Answer 1

as we know wavelengthλ=h/p
λ=h/mv             (as p=mv)
now the new wavelength λ' = h/mv'
                                           (as v'=2v)
                                        λ'=h/2mv
                                        λ'=1/2 of λ           (as λ=h/mv)
so wavelength becomes half when velocity is doubled

Answer 2

Explanation:

The relation between the wavelength and the velocity of a wave comes from the concept of De- broglie concept as :

$\lambda=\dfrac{h}{p}$

Where

p is the momentum of the particle

h is the Planck's constant

Since, p = mv

$\lambda=\dfrac{h}{mv}$

If velocity is doubled, v' = 2v

$\lambda=\dfrac{h}{mv'}$

$\lambda=\dfrac{h}{2mv}$

$\lambda=\dfrac{1}{2}\dfrac{h}{mv}$

It is clear from the above equation, that if the velocity of the particle is doubled, its wavelength becomes half. Hence, this is the required solution.