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An exoplanet's habitability is heavily dependent on it's hability to hold a suitable atmosphere. Earth's atmosphere is composed mostly of Hydrogen and Oxygen gas which allows for life. However, some of the gas might escape earth's atmosphere if it attains enough speed to overcome the gravitational pull, a process known as Jeans escape.
", "advice": "The mean spead is the average speed of the molecules. That is if you had 100 molecules and added all the speeds of each individual molecule and divided by 100 you would get this speed. The peak speed is the most likely measured speed, i.e. pick a random molecule out of those 100 and you are more likely to measure peak speed than you are any other. The formulas are given in page 62 of the lecture notes.
The mass of an Oxygen molecule = molar mass of oxygen molecule/ Avogrado's number.
in grams
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", "templateType": "number"}, "peak_vel": {"name": "peak_vel", "group": "Ungrouped variables", "definition": "sqrt((2*(1.381*10^(-23))*(temp+273.15))/(pi*((32/1000)/(6.0222*10^(23)))))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["mass_earth", "radius_earth", "g_constant", "esc_velocity", "M_mass_o2", "temp", "mean_vel", "boltz", "peak_vel"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "A projectile with mass $m$ will escape from the surface of a planet if it is launched upwards with a velocity, called escape velocity, of $v_e=\\sqrt{2\\frac{GM}{R_p}}$ where $G$ is the gravitational constant, $R_p$ is the radius of the planet and $M_p$ the mass of the planet. Calculate the escape velocity of a projectile on planet earth given that $G=6.670\\times10^{-11}~\\frac{Nm^2}{{Kg}^2}$, $M=5.970\\times10^{27}~g$ and $R_p=6370~km$. Type your answer in $\\frac{m}{s}$ to the nearest integer.
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What is the peak speed of Oxygen molecules at {temp}$^\\circ\\text{C}$?. Type your answer in $\\frac{m}{s}$ and rounded to the nearest integer.
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