Question

An atom of a particular element is traveling at 4.90 % of the speed of light. The de Broglie wavelength is found to be 3.01 fm. What is the identity of the element?

Give name or symbol of the element.

The speed of the atom was determined to have a variance of

Answer 1

For de Broglie equation :

$\Lambda = h/m\upsilon$

h = planck's constant, mass of the electron, v = velocity of the electron

v = 4.9% of 3 X 10^8 = 14700000 m

h = 6.626 X 10^-34Js

lambda , wavelength = 3.01 femto meter = 3.01 X 10^-15 m

therefore $m = h/\Lambda \upsilon$ = 6.626 X 10^-34 Js / 3.01 x 10^-15 x 14700000 = 0.0149 X 10^-24 kg

b)

heisenberg uncertainity pronciple : $\Delta x.\Delta \left ( m\upsilon \right ) \geqslant h/4\Pi$

$\Delta x. \geqslant h/4\Pi \Delta \left ( m\upsilon \right )$ = 6.6 X 10^-34Js /4 x 3.14 x 0.0149 X 10^-24 x 2.47 X 10^5 = 1.4 x 10^-6