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Sudikshya Pant

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## Homework Statement

:[/B]*An astronaut visiting Jupiter’s satellite Europa leaves a canister of 1.20 mol of nitrogen gas 28.0 g/mol^2 at 25.0°C on the satellite’s surface. Europa has no significant atmosphere, and the acceleration due to gravity at its surface is 1.30 m/s2. The canister springs a leak, allowing molecules to escape from a small hole. (a) What is the maximum height (in km) above Europa’s surface that is reached by a nitrogen molecule whose speed equals the rms speed? Assume that the molecule is shot straight up out of the hole in the canister, and ignore the variation in g with altitude. (b) The escape speed from Europa is 2025 m/s. Can any of the nitrogen molecules escape from Europa and into space?*

## Homework Equations

:[/B]

*v_rms =sqrt(3kT/m)*

where, m is the mass of a molecule in kg

where, m is the mass of a molecule in kg

OR

where, M is the molar mass in kg

*v_rms =sqrt(3RT/M)*where, M is the molar mass in kg

## The Attempt at a Solution

;[/B]Basically, I used the above formula and got the value for root mean square velocity as 515 m/s. Then, I tried to use Newton's law to get the height which is 102 km. For part (b) we might have to find the maximum velocity that a nitrogen molecule can have and when that molecule escapes the chances of nitrogen might be high. But how to get that velocity?I need some help for part (b). The velocity obtained must greater than the escape velocity. But how do we obtain the maximum velocity?

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