a) Find the probability that a molecule will travel a distance at least equal to the...
a) Find the probability that a molecule will travel a distance at least equal to the mean free path before its next collision.
b)After what distance of travel since the last collision is the probability of having suffered the next collision equal to 1/2?
Given the answer in terms of mean free path.
Homework Answers
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a) Find the probability that a molecule will travel a distance
at least equal to the...
In the following table are given the calculated mean free paths, collision diameters, and ratios of...
In the following table are given the calculated mean free paths, collision diameters, and ratios of mean free path to collision diameter for four gaseous molecules all at the same temperature and pressure. Determine from this table what general relationship predicts the ratio of mean free path to collision diameter. Molecule Mean free path (m/collision) 1.1 x 107 4.2 x 10+ 7.2 x 10 9.1 x 10 Collision diameter (m) 2.7 x 10-0 4.5 x 10-10 H co, Ratio of...
q 8.3 Show that particles hitting a plane boundary have travelled a distance 2 lambda/3 perpendicular...
q 8.3
Show that particles hitting a plane boundary have travelled a distance 2 lambda/3 perpendicular to the plane since their last collision, on average. A diffuse cloud of neutral hydrogen atoms in space has a temperature of 50 K and number density 500 cm^-3. Estimate the mean scattering time (in years) between hydrogen atoms in the cloud. Estimate the mean free path (in astronomical units).
The probability that an atom moving with speed v sutters a collision with another atom in...
The probability that an atom moving with speed v sutters a collision with another atom in the very next interval of time dt is vdt/e, where is a constant. (a) Show that the probability that an atom travels a distance svt in time t without undergoing any collisions is e (b) The probability that the atom undergoes its first collision in the distance interval between s and s + ds is P(s)ds. Find P(s) (c) Find 〈s) and 〈say in...
b) A loaded dice never lands showing the number 2, lands showing 6 with probability 1/3,...
b) A loaded dice never lands showing the number 2, lands showing 6 with probability 1/3, and all other numbers with probability 1/6. i) Calculate the probability that 3 such loaded dice land showing the same number 4 marks] Calculate the probability that when one such loaded dice is thrown together 3 marks] ii) with a fair dice they land showing the same number. c) The mean free path of a hydrogen molecule in air is 110 nm at standard...
The distance X between trees in a given forest has a probability density function given f...
The distance X between trees in a given forest has a probability density function given f (x) cex/10, x >0, and zero otherwise with measurement in feet i) Find the value of c that makes this function a valid probability density function. [4 marks] ii) Find the cumulative distribution function (CDF) of X. 5 marks What is the probability that the distance from a randomly selected tree to its nearest neighbour is at least 15 feet. iii) 4 marks) iv)...
Problem 3 - Mean free path (8 marks) Let's assume the opacity inside of a star...
Problem 3 - Mean free path (8 marks) Let's assume the opacity inside of a star is constant. The optical depth is T = not where o is the collisional cross-section of an ion. If the optical depth is T = 1, then the photon can't go very far before it's scattered. We write the mean free path as L which is the average distance a photon can go before being scattered. a. If the conditions in the Sun have...
In a certain particle accelerator, protons travel around a circular path of diameter D in an evacuated chamber, whose residual gas is at temperature T and pressure p. Assuming T is given in Kelvin an...
In a certain particle accelerator, protons travel around a circular path of diameter D in an evacuated chamber, whose residual gas is at temperature T and pressure p. Assuming T is given in Kelvin and p in pascals, calculate the number n of gas molecules per cubic meter under these conditions, what is the mean free path λ of the gas molecules if the molecular diameter is d. State your answers in terms of the given variables, using the Boltzmann...
The size of fish is very important to commercial fishing. A study conducted in 2012 found...
The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm (Ovegard, Berndt & Lunneryd, 2012). Assume the length of fish is normally distributed. Round the probabilities to four decimal places. It is possible with rounding for a probability to be 0.0000. a.) Find the probability that an Atlantic cod has...
5. A diatomic molecule (like H2) can be modeled as two atoms of equal mass m,...
5. A diatomic molecule (like H2) can be modeled as two atoms of equal mass m, connected by a rigid massless rod of length a. The system is free to rotate in 3-D. I claim the moment of inertia of this molecule around its ceater of mass is a. (Feel free to convince yourself that factor of k is coect!) Big hint if you 're having trouble getting started: this problem is directly related to McIntyre's Ch A) The energy...
Consider the following two-caraccident: Two cars of equal mass collide at an intersection. Driver E was traveling ea...
Consider the following
two-caraccident: Two cars of equal mass collide at an intersection. Driver E was traveling
eastward, anddriver N, northward. After the collision, the two cars
remainjoined together and slide, with locked wheels, before coming
torest. Police on the scene measure the length of the skid marks to be 9 meters. The coefficient
offriction between the locked wheels and the road is equal to
0.9.
Each driver claims that hisspeed
was less than 14 meters per second (50 mph)....
In the following table are given the calculated mean free paths, collision diameters, and ratios of mean free path to collision diameter for four gaseous molecules all at the same temperature and pressure. Determine from this table what general relationship predicts the ratio of mean free path to collision diameter. Molecule Mean free path (m/collision) 1.1 x 107 4.2 x 10+ 7.2 x 10 9.1 x 10 Collision diameter (m) 2.7 x 10-0 4.5 x 10-10 H co, Ratio of...
q 8.3
Show that particles hitting a plane boundary have travelled a distance 2 lambda/3 perpendicular to the plane since their last collision, on average. A diffuse cloud of neutral hydrogen atoms in space has a temperature of 50 K and number density 500 cm^-3. Estimate the mean scattering time (in years) between hydrogen atoms in the cloud. Estimate the mean free path (in astronomical units).
The probability that an atom moving with speed v sutters a collision with another atom in the very next interval of time dt is vdt/e, where is a constant. (a) Show that the probability that an atom travels a distance svt in time t without undergoing any collisions is e (b) The probability that the atom undergoes its first collision in the distance interval between s and s + ds is P(s)ds. Find P(s) (c) Find 〈s) and 〈say in...
b) A loaded dice never lands showing the number 2, lands showing 6 with probability 1/3, and all other numbers with probability 1/6. i) Calculate the probability that 3 such loaded dice land showing the same number 4 marks] Calculate the probability that when one such loaded dice is thrown together 3 marks] ii) with a fair dice they land showing the same number. c) The mean free path of a hydrogen molecule in air is 110 nm at standard...
The distance X between trees in a given forest has a probability density function given f (x) cex/10, x >0, and zero otherwise with measurement in feet i) Find the value of c that makes this function a valid probability density function. [4 marks] ii) Find the cumulative distribution function (CDF) of X. 5 marks What is the probability that the distance from a randomly selected tree to its nearest neighbour is at least 15 feet. iii) 4 marks) iv)...
Problem 3 - Mean free path (8 marks) Let's assume the opacity inside of a star is constant. The optical depth is T = not where o is the collisional cross-section of an ion. If the optical depth is T = 1, then the photon can't go very far before it's scattered. We write the mean free path as L which is the average distance a photon can go before being scattered. a. If the conditions in the Sun have...
In a certain particle accelerator, protons travel around a circular path of diameter D in an evacuated chamber, whose residual gas is at temperature T and pressure p. Assuming T is given in Kelvin and p in pascals, calculate the number n of gas molecules per cubic meter under these conditions, what is the mean free path λ of the gas molecules if the molecular diameter is d. State your answers in terms of the given variables, using the Boltzmann...
The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm (Ovegard, Berndt & Lunneryd, 2012). Assume the length of fish is normally distributed. Round the probabilities to four decimal places. It is possible with rounding for a probability to be 0.0000. a.) Find the probability that an Atlantic cod has...
5. A diatomic molecule (like H2) can be modeled as two atoms of equal mass m, connected by a rigid massless rod of length a. The system is free to rotate in 3-D. I claim the moment of inertia of this molecule around its ceater of mass is a. (Feel free to convince yourself that factor of k is coect!) Big hint if you 're having trouble getting started: this problem is directly related to McIntyre's Ch A) The energy...
Consider the following
two-caraccident: Two cars of equal mass collide at an intersection. Driver E was traveling
eastward, anddriver N, northward. After the collision, the two cars
remainjoined together and slide, with locked wheels, before coming
torest. Police on the scene measure the length of the skid marks to be 9 meters. The coefficient
offriction between the locked wheels and the road is equal to
0.9.
Each driver claims that hisspeed
was less than 14 meters per second (50 mph)....
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