Question

What will happen to the wavelength associated with the moving particle if its velocity is reduce to half

Answer 1

If it's velocity is reduced to half then wavelength will increase by 2

Answer 2

Given: the wavelength of the moving particle, λ₁

           The velocity of the moving particle, v₁, and v₂ = v₁/2

To Find: wavelength, when the velocity is reduced to half, λ₂

Solution:

To calculate wavelength, the formula used:

• λ = h / m x v
• here, h is the Plank's constant.

                 m is the mass of the particle

Applying the above formula, when velocity is v₁ :

λ₁ = h / m x v₁                                  ⇒ 1

When velocity is reduced to half:

v₂ = v₁ / 2

λ₂ = h / m x v₂

Putting the value of v₂ in above equation:

λ₂ = h / (m x v1/2)

λ₂ = 2 x (h / m x v₁)                                ⇒ 2

On comparing equations 1 and 2 :

λ₂ = 2 x λ₁

Hence, when the velocity is reduced to half, the wavelength of the moving particle will be double or 2 times of its original value.