Question

The respective speeds of molecules are 2, 4, 6, 8 km/s. The ratio of their rms velocity and average velocity will be

Answer 1

$\bigstar$ Answer $\bigstar$

⇒ Speeds of molecules are 2, 4, 6, 8 km/s

Where,

$\rm v_1 = 2\;km/s\\v_2 = 4\;km/s\\v_3 = 6\;km/s\\v_4 = 8\;km/s$

Average velocity of the molecules ($\rm v_a_v$)

$\implies \rm \dfrac{v_1+v_2+v_3+v_4}{4}$

$\implies \rm \dfrac{2+4+6+8}{4}$

$\implies \rm \dfrac{20}{4}$

$\implies \rm 5$

$\orange{\boxed{\rm v_a_v = 5 \;km/s}}$

Root mean square velocity of the molecules ($\rm v_r_m_s$)

$\implies \rm \sqrt{\dfrac{(v_1)^2+(v_2)^2+(v_3)^2+(v_4)^2}{4} }$

$\implies \rm \sqrt{\dfrac{(2)^2+(4)^2+(6)^2+(8)^2}{4} }$

$\implies \rm \sqrt{\dfrac{4+16+36+64}{4} }$

$\implies \rm \sqrt{\dfrac{120}{4} }$

$\implies \rm \sqrt{30}$

$\implies \rm 5.47$

$\blue{\boxed{\rm v_r_m_s = 5.47\;km/s}}$

Hence,

The ratio of their rms velocity ($\rm v_r_m_s$) and average velocity($\rm v_a_v$) is

$\implies \rm \dfrac{v_r_m_s}{v_a_v} = \dfrac{5.47}{5}$

The ratio will be,

$\implies {\green{\boxed{\rm 5.47\;:\;5}}$