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Using the Heisenberg uncertainty principle, arrange the following particles in the order of increasing lowest energy possible.
$(I)$ An electron in $H _{2}$ molecule
$(II)$ A hydrogen atom in a $H _{2}$ molecule
$(III)$ A proton in the carbon nucleus
$(IV)$ $A H _{2}$ molecule within a nanotube
$I < III < II < IV$
$IV < II < I < III$
$II < IV < III < I$
$IV < I < II < 111$
Solution
$(b)$ $A H _{2}$ molecule in a nanotube is bound only by adhesive forces. So, its energy is least.
A hydrogen atom in a $H _{2}$ molecule is bound by interatomic forces. So, its energy is less than the energy of an electron in $H _{2}$ molecule.
Proton in a carbon nucleus is bound because of strong nuclear forces. So, its energy is largest.
$\therefore$ Correct order is $IV < II < I < Ill$.
