Question

An atom of an unknown element travels at 0.99% of the speed of light. Its de Broglie wavelength is 3.29x10^{-3}​−3​​ pm. What is the element's symbol?

Answer 1

debroglies equation

   l = h/P

   l = h/mv   (P= mv)

l = wavelength of wave associated with atom of an unknown element   = 3.29*10^-3 pm = 3.29*10^-15 m   (1 pm = 10^-12 m)

v = speed of atom of an unknown element = 3*10^8*0.99/100 = 2.97*10^6 m/s

m = mass of atom of an unknown element = ? kg

h = planks constant = 6.625*10^-34 j.s

(3.29*10^-15) = ((6.625*10^-34)/(m*2.97*10^6))

   m = 6.78*10^-26 kg

     = 6.78*10^-23 g

atomicmass of element = m*N = 6.78*10^-23*6.023*10^23 = 40.8 g/mol

element symbol = Calcium(Ca)