If the temperature of argon gas is 400 K and the average velocity of argon is twice that of radon what is the temperature of radon gas?

Question

The answer key says it is 555 K. How do I approach this question? 

Answer 1

Temperature is proportional to the kinetic energy of the gas particles.    So to solve this problem you will have to know the relative mass and velocity of the two atoms of gas

 

KE1 : KE2 =  T1:T2;

 

Note that Var = 2Vne

 

1/2(m_Ar * (2V_Ne)²⁾/  [1/2(m_Ne *( V^Ne)_²]

 

(40/222) * 4 =   400/T_Rn

 

T_Rn =   400/(160/222) = 555