Question

A particle of mass 1mg has the same wavelength as an electron moving with a velocity of 3times10^(8)ms^(-1)* The velocity of the particle is (mass of electron =9.1times10^(-8)kg)​

Answer 1

Given : mass of particle (m₁) = 1 mg  or 10⁻³ Kg .

             Let velocity of the particle be v₁ .

            velocity of electron (v₂) = 3x10⁸ m/s .

            mass of electron (m₂) = 9.1 x 10⁻⁸ Kg .

We know the relation wave length and linear momentum according to de-Broglie .

λ = h / (mv)

λ - wave length

h - Plank's constant

m - mass of particles

v - velocity of particles

given both the particles have same wave length.

⇒  λ₁ = λ₂

⇒ h/(m₁ v₁) = h/(m₂ v₂)

⇒ m₁ v₁ = m₂ v₂

⇒ 10⁻³ Kg x v₁ = 9.1 x 10⁻⁸ Kg x 3x10⁸ m/s

   ∴ v₁ = 2.73 x 10⁴ m/s.

HOPE THIS HELPS YOU !!   : )