Root Mean Square Velocity of Gases

  • #1

Homework Statement:

At what temperature will the RMS velocity of Oxygen Molecules become just sufficient for escaping from the Earth's atmosphere?
Given :
Mass of one Oxygen molecule=2.76*(10^-26)kg
Boltzmann Constant Kb=1.38*(10^-23)J/K
OPTIONS:
1. 25080 K
2. 83600 K
3. 12540 K
4. 50160 K

Relevant Equations:

Vrms=√{3RT/M}=√{3KbT/m}
Escape Velocity=√{2gRe}
Re=Radius of Earth
This question came in NEET Exam 2018.Now my first query is that in the question,the mass of one Oxygen molecule is given wrong.Its exactly half it's true value.I don't think anybody has noticed this before because I couldn't find any change in the printed question on so many different books.
Also all the options are also incorrect.For anyone who is hearing about NEET for the first time, it is the All Indian Medical Exam.There are negative marks for wrong answers while unattemped questions are not marked.
What should I do?Are they expecting us to use the value which they have provided?
Then by equating Vrms and Vescape,Temperature is coming out to be that of option 2.I have no problem with the solving part but I don't know whether it will be proper to ask this horrible question in such an Awesome platform.
 

Answers and Replies

  • #2
haruspex
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Homework Statement:: At what temperature will the RMS velocity of Oxygen Molecules become just sufficient for escaping from the Earth's atmosphere?
Given :
Mass of one Oxygen molecule=2.76*(10^-26)kg
Boltzmann Constant Kb=1.38*(10^-23)J/K
OPTIONS:
1. 25080 K
2. 83600 K
3. 12540 K
4. 50160 K
Relevant Equations:: Vrms=√{3RT/M}=√{3KbT/m}
Escape Velocity=√{2gRe}
Re=Radius of Earth

This question came in NEET Exam 2018.Now my first query is that in the question,the mass of one Oxygen molecule is given wrong.Its exactly half it's true value.I don't think anybody has noticed this before because I couldn't find any change in the printed question on so many different books.
Also all the options are also incorrect.For anyone who is hearing about NEET for the first time, it is the All Indian Medical Exam.There are negative marks for wrong answers while unattemped questions are not marked.
What should I do?Are they expecting us to use the value which they have provided?
Then by equating Vrms and Vescape,Temperature is coming out to be that of option 2.I have no problem with the solving part but I don't know whether it will be proper to ask this horrible question in such an Awesome platform.
I should think few students would know that mass value was wrong. Luckily, there is no option corresponding to the correct value, so you can be sure the examiners have used the atomic weight by mistake.
I assume you are being asked by your education facility to answer this as homework. Give the expected answer, option 2. If there is the means to do so, let them and the NEET board know of the error.
 
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