In the previous equation, what is the rms speed of each type of molecules?

Options

A. `21 km//s`
B. `1.62 km//s`
C. `4.62 km//s`
D. `3.24 km//s`

Answer

B

Explanation

The root-mean square velocity can be calculated from the kinetic energy:
We know `bar(K) = 1/2 m_(0)v_(rms)^(2) implies v_(rms) = sqrt((2bar(K)))/(m_0))`
So, `v_(rms) = sqrt((1.75xx10^(-21)J)/(m_0))`..(i)
For helium, mass of a molecule
`(m_0)_(He) = (4.00g//"mol")/(6.02 xx 10^(23) "molecules"//"mol") = 6.64xx10^(-24)g`
Substituting into eq. (i) we get
We find root-mean square velocity for helium, `v_(rms) =1.62 km//s`.