Two molecules of a gas have speeds of $$9$$ x $$106$$ $$ms-l$$ and $$1$$ × $$106$$ $$ms-1$$ respectively. What is the root mean square speed of these molecules?

Question

Two molecules of a gas have speeds of $$9$$ x $$106$$ $$ms-l$$ and $$1$$ × $$106$$ $$ms-1$$ respectively. What is the root mean square speed of these molecules?

Infinity Learn · Accepted Answer

For $$n-molecules$$, we know thatvrms $$=$$ $$v12+v22+v23+$$....$$+$$ $$vn2n$$[vrms $$=$$ root mean square velocity]where $$v1$$, $$v2$$, $$v3$$,...vn are individual velocities of $$n-molecules$$ of the gas.For two molecules, vrms $$=$$ $$v21+v222$$[$$v1$$, $$v2$$, $$v3$$,...vn are individual velocity]Given, $$v1$$ $$=$$ $$9$$ × $$106$$ $$m/s$$ and $$v2$$ $$=$$ $$1$$×$$106$$ $$m/s$$∴ vrms $$=$$ $$(9$$×$$106)2+(1$$×$$106)22$$ $$=$$ $$41$$ × $$106$$ $$m/s$$

Two molecules of a gas have speeds of $9 x 10^{6} {ms}^{- l}$ and $1 \times 10^{6} {ms}^{- 1}$ respectively. What is the root mean square speed of these molecules?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Two molecules of a gas have speeds of 9 x 106 ms-l and 1 × 106 ms-1 respectively. What is the root mean square speed of these molecules?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Two molecules of a gas have speeds of $9 x 10^{6} {ms}^{- l}$ and $1 \times 10^{6} {ms}^{- 1}$ respectively. What is the root mean square speed of these molecules?