A particle of mass 2 mg has the same wavelength as a neutron moving with a velocity of 3 10^5 ~ms ⁻¹ . The velocity of the particle is (mass of neutron is 1.67 10⁻²⁷ Kg )

Step-by-step solution

The de Broglie wavelength is given by the relation = h mv . Since the particle and the neutron have the same wavelength, we have _ p = _ n , which implies m_ p v_ p = m_ n v_ n . Given values are: Mass of particle m_ p = 2 mg = 2 10⁻⁶ kg . Mass of neutron m_ n = 1.67 10⁻²⁷ kg . Velocity of neutron v_ n = 3 10^5 ms ⁻¹ . Substituting these values into the equation v_ p = m_ n v_ n m_ p : v_ p = (1.67 10⁻²⁷ kg ) (3 10^5 ms ⁻¹) 2 10⁻⁶ kg v_ p = 5.01 10⁻²² 2 10⁻⁶ ms ⁻¹ v_ p = 2.505 10⁻¹⁶ ms ⁻¹ Rounding to the nearest pr