Question

A molecule consists of two atoms each of mass 'm' and separated by a distance 'd'. At room temperature the average rotational kinetic energy is 'E', then its angular frequency is ______.

Options

• `2/"d" sqrt("E"/"m")`

• `sqrt("m"/"Ed")`

• `"d"/2 sqrt("m"/"E")`

• `sqrt("Ed"/"m"`

Answer 1

A molecule consists of two atoms each of mass 'm' and separated by a distance 'd'. At room temperature the average rotational kinetic energy is 'E', then its angular frequency is `underline(2/"d" sqrt("E"/"m")`.

Explanation:

MI of molecule = `"m"("d"/2)^2 + "m"("d"/2)^2`

`="md"^2/2`

Now, `1/2 "I"omega^2` = E

`omega = sqrt((2"E")/"I") = sqrt((2 xx "E" xx 2)/"md"^2)`

`= 2/"d" sqrt("E"/"m")`