Question

Jupiter's exosphere has a temperature of about 840.0 K. What is the thermal speed of hydrogen (in km/s) in Jupiter's exosphere? The mass of a hydrogen atom is 1.67 x 10^-27 kg and Boltzmann's constant is k = 1.38 × 10^-23 Joule/Kelvin.

I need help with this I don't understand. I get this is the formula: (Thermal Speed)^2 = 2 · Boltzman constant · Temperature / Mass

But I am getting it wrong.

Answer 1

Here, we are required to determine the thermal speed(in km/s) of Jupiter's exosphere.

The thermal speed (in km/s) is 3.726km/s.

First, The thermal speed is related to the temperature and mass of hydrogen by the formular:

(Thermal speed)² =

(2 × Boltzman constant × Temperature)/Mass.

According to the question,

• Boltzman constant, k = 1.38 × 10^-23

• Temperature, T = 840.0k

• and Mass = 1.67 × 10^-27 kg.

Therefore, (thermal speed)²

= (2 × 1.38 × 10^-23 × 840)/1.67 × 10^-27

(Thermal speed)² = 1388.26 × 10⁴

Therefore, (thermal speed) = √1388.26 × 10⁴

Therefore, thermal speed = 3725.9m/s

By converting, thermal speed = 3.726km/s.

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