Final answer:
A nitrogen molecule with an average translational kinetic energy of 6.2 x 10⁻²¹ J and a mass of 4.7 x 10⁻²⁶ kg would rise approximately 1.32 meters if it could shoot straight up without hitting other air molecules.
Step-by-step explanation:
The student asked about how high a nitrogen molecule with an average translational kinetic energy (KE) of 6.2 x 10⁻²¹ J at sea level would rise if it shot straight up without hitting other air molecules. This question is a Physics problem involving the conversion of kinetic energy to gravitational potential energy. The mass of a nitrogen molecule, N₂, is 4.7 x 10⁻²⁶ kg, and using this, we can calculate the height it would reach by setting the kinetic energy equal to the potential energy (mgh).
To calculate the height, we use the formula KE = mgh, where m is the mass of the molecule, g is the acceleration due to gravity (approximately 9.81 m/s² near the Earth's surface), and h is the height. By rearranging the formula to solve for h, we get h = KE / (mg). Substituting the provided values, we find:
h = (6.2 x 10⁻²¹ J) / (4.7 x 10⁻²⁶ kg x 9.81 m/s²)
h = approximately 1.32 meters. Therefore, the nitrogen molecule would rise to about 1.32 meters before its kinetic energy is completely converted to gravitational potential energy, and it begins to fall back down.