Question

A hydrogen atom has mass $1.68\times {10}^{-27}$kg. When attached to a certain massive molecule it oscillates with a frequency ${10}^{14}$ Hz and with an amplitude ${10}^{-9}$ cm. Find the force acting on the hydrogen atom.

• A. $2.21\times {10}^{-9}$ N
• B. $3.31\times {10}^{-9}$ N
• C. $4.42\times {10}^{-9}$ N
• D. $6.63\times {10}^{-9}$ N

Answer 1

The correct option is D $6.63\times {10}^{-9}$ N

${\omega }^2=\frac{k}{m}\Rightarrow {\left(2\pi f\right)}^2=\frac{k}{m}\Rightarrow k=4{\pi }^2{f}^{2}m$
and
$F=k{x}_0=4{\pi }^2{f}^{2}m{x}_0\Rightarrow F=4\times {\pi }^2\times {10}^{28}\times 1.68\times {10}^{-27}\times {10}^{-11}N\Rightarrow F=6.63\times {10}^{-9}N$