Question

Titan's exosphere has a temperature of about 172 K. What is the thermal speed of hydrogen (in km/s) in Titan''s exosphere? The mass of a hydrogen atom is 1.67 × 10-27 kg and Boltzmann's constant is k = 1.38 × 10-23 Joule/Kelvin.

Answer 1

Thermal speed, v = 2.064 km/s

Step-by-step explanation:

It is given that,

Temperature of Titan's exosphere, T = 172 K

Mass of the hydrogen atom,
`M=1.67* 10^(-27)\ kg`

Boltzmann's constant,
`k=1.38* 10^(-23)\ J/K`

Let v is the thermal speed of Hydrogen. It can be calculated using the following formula as :

`v=\sqrt{(3kT)/(M)}`

`v=\sqrt{(3* 1.38* 10^(-23)* 172)/(1.67* 10^(-27))}`

v = 2064.93 m/s

or

v = 2.064 km/s

Hence, the thermal speed of hydrogen in Titan's exosphere is 2.064 km/s.