The wavelength of a microscopic particle of mass (9.1 10⁻³¹ ~kg ) is (182 ~nm ), its kinetic energy in ( J ) is ( (h=6.625 10⁻³⁴ ~J ~s ) )

Step-by-step solution

Given, mass of particles (=9.1 10⁻³¹ ~kg ) Wavelength (( )=182 ~nm =182 10⁻⁹ ~m ) According to de-Broglie equation, ( aligned & = h m v v= h m v & = 6.625 10⁻³⁴ Js 91 10⁻³¹ ~kg 182 10⁻⁹ ~m & =0.004 10^6 ~m / s =4 10^3 ~m / s aligned ) Therefore, kinetic energy, ( aligned KE = 1 2 m v^2 & = 1 2 9 I 10⁻³¹ (4 10^3 )^2 & =7.28 10⁻²⁴ ~J aligned )