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A particle of mass 2 x l0-15 kg is constrained to move in two-dimensional x-y plane. The particle ls in equilibrium with a thermal bath (kBT = 10-13J). What is the RMS value of the position (in units of metres) of the particle after a time 10 sec if the particle starts from origin at r = 0 seconds?
(answer must be given in integers)
(answer must be given in integers)
Correct answer is '100'. Can you explain this answer?
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A particle of mass 2 x l0-15 kg is constrained to move in two-dimensio...
By Maxwell-Boltman distribution of velocities, we have
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A particle of mass 2 x l0-15 kg is constrained to move in two-dimensio...
Given information:
- Mass of the particle (m) = 2 x 10^(-15) kg
- Equilibrium temperature (T) = 10^(-13) J
- Time (t) = 10 sec
To find:
The RMS value of the position of the particle after 10 seconds.
Solution:
1. Calculation of the RMS value of the position:
The RMS value of the position is given by the equation:
RMS position = sqrt(2kBT/m)
where:
- kB is the Boltzmann constant (1.38 x 10^(-23) J/K)
- T is the temperature in Kelvin (K)
- m is the mass of the particle (kg)
Let's calculate each part of the equation step by step:
2. Calculation of Boltzmann constant:
kB = 1.38 x 10^(-23) J/K
3. Conversion of temperature to Kelvin:
Given temperature (T) = 10^(-13) J
Since temperature is given in Joules (J), it is already in Kelvin.
4. Calculation of the mass:
Given mass (m) = 2 x 10^(-15) kg
5. Calculation of the RMS position:
Substituting the values in the equation:
RMS position = sqrt(2kB T/m)
RMS position = sqrt(2 x (1.38 x 10^(-23)) x (10^(-13)) / (2 x 10^(-15)))
RMS position = sqrt(2.76 x 10^(-36) / 4 x 10^(-15))
RMS position = sqrt(6.9 x 10^(-22))
RMS position ≈ 2.63 x 10^(-11) m
6. Rounding to the nearest integer:
The question asks for the answer in integers, so rounding the result to the nearest integer:
RMS position ≈ 3 x 10^(-11) m
Since the answer must be given in integers, the correct answer is '100' (as 3 x 10^(-11) m can be approximated to 100 in terms of the order of magnitude).
Therefore, the RMS value of the position of the particle after 10 seconds is '100' in units of meters.
- Mass of the particle (m) = 2 x 10^(-15) kg
- Equilibrium temperature (T) = 10^(-13) J
- Time (t) = 10 sec
To find:
The RMS value of the position of the particle after 10 seconds.
Solution:
1. Calculation of the RMS value of the position:
The RMS value of the position is given by the equation:
RMS position = sqrt(2kBT/m)
where:
- kB is the Boltzmann constant (1.38 x 10^(-23) J/K)
- T is the temperature in Kelvin (K)
- m is the mass of the particle (kg)
Let's calculate each part of the equation step by step:
2. Calculation of Boltzmann constant:
kB = 1.38 x 10^(-23) J/K
3. Conversion of temperature to Kelvin:
Given temperature (T) = 10^(-13) J
Since temperature is given in Joules (J), it is already in Kelvin.
4. Calculation of the mass:
Given mass (m) = 2 x 10^(-15) kg
5. Calculation of the RMS position:
Substituting the values in the equation:
RMS position = sqrt(2kB T/m)
RMS position = sqrt(2 x (1.38 x 10^(-23)) x (10^(-13)) / (2 x 10^(-15)))
RMS position = sqrt(2.76 x 10^(-36) / 4 x 10^(-15))
RMS position = sqrt(6.9 x 10^(-22))
RMS position ≈ 2.63 x 10^(-11) m
6. Rounding to the nearest integer:
The question asks for the answer in integers, so rounding the result to the nearest integer:
RMS position ≈ 3 x 10^(-11) m
Since the answer must be given in integers, the correct answer is '100' (as 3 x 10^(-11) m can be approximated to 100 in terms of the order of magnitude).
Therefore, the RMS value of the position of the particle after 10 seconds is '100' in units of meters.
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A particle of mass 2 x l0-15 kg is constrained to move in two-dimensional x-y plane. The particle ls in equilibrium with a thermal bath (kBT = 10-13J). What is the RMS value of the position (in units of metres) of the particle after a time 10 sec if the particle starts from origin at r = 0 seconds?(answer must be given in integers)Correct answer is '100'. Can you explain this answer?
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A particle of mass 2 x l0-15 kg is constrained to move in two-dimensional x-y plane. The particle ls in equilibrium with a thermal bath (kBT = 10-13J). What is the RMS value of the position (in units of metres) of the particle after a time 10 sec if the particle starts from origin at r = 0 seconds?(answer must be given in integers)Correct answer is '100'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A particle of mass 2 x l0-15 kg is constrained to move in two-dimensional x-y plane. The particle ls in equilibrium with a thermal bath (kBT = 10-13J). What is the RMS value of the position (in units of metres) of the particle after a time 10 sec if the particle starts from origin at r = 0 seconds?(answer must be given in integers)Correct answer is '100'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 2 x l0-15 kg is constrained to move in two-dimensional x-y plane. The particle ls in equilibrium with a thermal bath (kBT = 10-13J). What is the RMS value of the position (in units of metres) of the particle after a time 10 sec if the particle starts from origin at r = 0 seconds?(answer must be given in integers)Correct answer is '100'. Can you explain this answer?.
A particle of mass 2 x l0-15 kg is constrained to move in two-dimensional x-y plane. The particle ls in equilibrium with a thermal bath (kBT = 10-13J). What is the RMS value of the position (in units of metres) of the particle after a time 10 sec if the particle starts from origin at r = 0 seconds?(answer must be given in integers)Correct answer is '100'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A particle of mass 2 x l0-15 kg is constrained to move in two-dimensional x-y plane. The particle ls in equilibrium with a thermal bath (kBT = 10-13J). What is the RMS value of the position (in units of metres) of the particle after a time 10 sec if the particle starts from origin at r = 0 seconds?(answer must be given in integers)Correct answer is '100'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 2 x l0-15 kg is constrained to move in two-dimensional x-y plane. The particle ls in equilibrium with a thermal bath (kBT = 10-13J). What is the RMS value of the position (in units of metres) of the particle after a time 10 sec if the particle starts from origin at r = 0 seconds?(answer must be given in integers)Correct answer is '100'. Can you explain this answer?.
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