Consider an atom diffuses in a $3$D simple cubic lattice by a random walk mechanism. The atom jumps $6$x$10$^-5 times per second at $300$K and $3$x$104$ times per second at $600$K$.$

Assuming that the vibrational frequency $($f$)$ of the atom keeps constant for all the 

temperatures considered.

$($a$)$ At what temperature will the jumping be increased to $1\mathrm{.}6$ times $107$ times per second?

$($b$)$ Considering the distance $($r$)$ that the atom can move away from its original position in $1$ minute at two different temperatures, $300$ K and $1500$ K$,$ what is the ratio of r at $1500$K to that at $300$K$?$

 

 

 

 

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