A molecule of hydrogen gas has a mass of 3351027kg and a dia

A molecule of hydrogen gas has a mass of 3.35×1027kg and a diameter of 1.48×1010m. What is the kinetic energy at which this molecule\'s de Broglie wavelength will be equal to its diameter?

What is the kinetic energy K0 at which this molecule\'s de Broglie wavelength will be equal to its diameter?

Solution

de Broglie wavelength = h/P , p = sqrt ( 2mKE)

m = 2*1.67*10^-27 kg

=> 1.48*10^-10 = 6.62*10^-34)/(sqrt (2*2*1.67*10^-27*KE))

=> KE =  (6.62*10^-34/(1.48*10^-10 ))^2/(2*2*1.67*10^-27) = 2.995*10^-21 J