Smoke particles in the air typically have masses on the order of 10-16 kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with a microscope. (a) Find the root-mean-square speed of Brownian motion for a particle with a mass of 3.00 * 10-16 kg in air at 300 K. (b) Would the root-mean-square speed be different if the particle were in hydrogen gas at the same temperature? Explain.

Smoke particles in the air typically have masses on the order of 10-16 kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with a microscope. (a) Find the root-mean-square speed of Brownian motion for a particle with a mass of 3.00 * 10-16 kg in air at 300 K. (b) Would the root-mean-square speed be different if the particle were in hydrogen gas at the same temperature? Explain.

Related questions

Q: The escape velocity from the Moon is much smaller than from Earth and is only 2.38 km/s. At what…

A: The escape velocity of the moon,(VM)=2.38 km/s=2.38 x 103 m/s ----(1) [Given] [Using 1 km=103 m]…

Q: Which of the following gases is most likely the unknown gas: He, CO, HF, HBr, or F2?

A: The root mean square velocity ( Vrms) can be determined by the formula Vrms= 3RTM ( where T=…

Q: Hydrogen gas is cooled to 100 K, while the pressure is reduced to 0.1 Pa. a) Determine the mean free…

A: Since your question have 4 subparts and first two subparts have 4 questions in total, we will solve…

Q: Suppose a Krypton atom (atomic mass = 83.8 u) near the surface of the Earth where the temperature is…

Q: Estimate the time needed for a glycine molecule (see Table 13−413−4 in the textbook) to diffuse a…

Q: a) What is the volume of the bubble at the surface? b) What is the root mean square speed of…

A: Boyle's Law Keeping the temperature constant, the volume occupied by a gas is inversely proportional…

Q: Escape velocity from the Moon is approximately 5310 miles per hour = 2.37 x 103 m/s. At certain…

Q: Much of the gas near the Sun is hydrogen nuclei. Its temperature would have to be 1.5 × 107 K for…

A: The root of the average of the molecular speed square is, Here, the root-mean-square speed is vrms,…

Q: What is the root-mean-square speed, in units of m/sec, of monatomic He atoms at a temperature of…

Q: By counting squares in the following figure, estimate the fraction of argon atoms at T = 300 K that…

Q: One mole of nitrogen has a mass of 28 g. Calculate the mean speed of the Maxwell-Boltzmann…

A: The mean speed of the Maxwell-Boltzmann distribution c = (8RT/(πM))1/2 M is molar mass R = 8.314…

Q: Assume that in gas diffusion experiment you place NH3 and HCl at the ends of a tube that is 11 cm…

Q: Suppose that the rms speed of carbon dioxide molecules, with molar mass of 44.0 g/mol, in a flame is…

A: Given that, The rms speed of carbon dioxide molecule, vrms=1.25×105 m/s Molar mass, M=44.0…

Q: The escape speed from the Moon is much smaller than from Earth and is only 2.38 km/s. At what…

A: The escape speed=2.38 km/s=2380 m/s. The molecular mass of chlorine molecules is M=70.91…

Q: In the hot gases of an automotive engine's cylinders, temperatures may exceed 3100 k. What would be…

A: Given In the hot gases of an automotive engine's cylinders, temperatures may exceed 3100 k. The mass…

Q: Consider neon, a noble gas whose molecules consist of single atoms of atomic mass 0.02 kg/mol. What…

Q: a) Calculate the mean free path in meters of a nitrogen molecule (with a mass m=4.68×10-26 kg)…

A: (a) Radius of the molecule is, r=3V4π13r=3nNA4πnV13r=34.68×10-26 kg28×10-3 kg·mol-16.023×10234π1025…

Q: The reaction rate for the prepupal development of male Drosophila is temperature-dependent. Assuming…

Q: The pressure unit 1 torr is comparable to 0.001 bar. In a sample of N₂ at this pressure and a…

A: Mean free path is the distance covered by free gas particle in between two consecutive collisions.…

Question

Smoke particles in the air typically have masses on the order of 10^-16 kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with a microscope. (a) Find the root-mean-square speed of Brownian motion for a particle with a mass of 3.00 * 10^-16 kg in air at 300 K. (b) Would the root-mean-square speed be different if the particle were in hydrogen gas at the same temperature? Explain.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

The root mean square velocity of an oxygen molecule is 1,302.27 m/s. Estimate the temperature at which it is located.
An argon-40 atom has a mass of 6.64 ✕ 10−26 kg. (a) What temperature (in K) would a gas composed entirely of argon-40 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from Earth, 1.12 ✕ 104 m/s? K (b) What temperature (in K) would a gas composed entirely of argon-40 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from the Moon, 2.37 ✕ 103 m/s? K
Determine how many times per second each molecule moving with rms speed would move back and forth across a 6.4 mm -long room on the average, assuming it made very few collisions with other molecules.To find vx use the equation v2=v2x+v2y+v2z and the fact that molecules have no preferred direction. vrms= 473 m/s
Suppose that an insulating container of air at room temperature and standard pressure is initially traveling at a speed v0 (perhaps in a car). We bring the container suddenly to rest. Assume that the air’s center-of-mass kinetic energy gets converted entirely to thermal energy in this process. (a) What is the air’s change in temperature ΔT in terms of kB, v0, and the average mass of an air molecule m? Determine such a relationship. (b) If v0 = 44 m / s, what is the numerical value of ΔT? The numerical value of ΔT is ______K.
What is the root-mean-square speed, in units of m/sec, of monatomic Ne atoms at a temperature of 24.1°C?
Dr. Chini's research group recently made an interesting discovery, while studying laser interactions with molecular gases. They found that nitrous oxide molecules (mass 44.013 g per mole) can reach temperatures exceeding 745 degrees Celsius after a interacting with a few closely-spaced (in time) laser pulses. At this temperature, what is the rms speed (in m/s) of a nitrous oxide molecule?
A vessel contains 1.00 × 104 oxygen molecules at 500 K. (a) Make an accurate graph of the Maxwell speed distribution function versus speed with points at speed intervals of 100 m/s. (b) Determine the most probable speed from thisgraph. (c) Calculate the average and rms speeds for the molecules and label these points on your graph. (d) From the graph, estimate the fraction of molecules with speeds in the range 300 m/s to 600 m/s.