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A collimated beam of pions originate from an accelerator and propagates in vacuum along a long straight beam pipe. The intensity of this beam was measured in the laboratory after a distance of 60 m and found to have dropped to one fourth of its intensity at the point of origin. If the proper half - life of a pion is 1.6 x 10-8 sec, the speed of the pions in the beam, as measured in the laboratory , must be nc. The value of n is _____
Correct answer is '0.99'. Can you explain this answer?
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A collimated beam of pions originate from an accelerator and propagate...
we know that
x = VΔt
x = VΔt
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A collimated beam of pions originate from an accelerator and propagate...
Given:
- Distance traveled by the pions: 60 m
- Intensity dropped to one fourth of its intensity at the point of origin
- Proper half-life of a pion: 1.6 x 10^-8 sec
To Find:
- The value of 'n', which represents the speed of the pions in the beam as measured in the laboratory
Explanation:
The intensity of a beam of particles decreases exponentially with distance traveled, according to the decay law. The decay law is given by the equation:
I = I₀ * e^(-λx)
Where:
- I is the intensity at a distance x
- I₀ is the initial intensity (at x = 0)
- λ is the decay constant
In this case, the intensity has dropped to one fourth of its intensity at the point of origin after traveling a distance of 60 m. Using this information, we can write the equation:
(1/4) * I₀ = I₀ * e^(-λ * 60)
Simplifying the equation, we get:
e^(-λ * 60) = 1/4
Taking the natural logarithm (ln) of both sides, we have:
-λ * 60 = ln(1/4)
Solving for λ, we get:
λ = -ln(1/4) / 60
The proper half-life (t₀.₅) of a particle is related to the decay constant (λ) by the equation:
t₀.₅ = ln(2) / λ
Substituting the value of λ, we can solve for t₀.₅:
t₀.₅ = ln(2) / (-ln(1/4) / 60)
Simplifying the equation, we get:
t₀.₅ = 60 * ln(2) / ln(4)
The speed of a particle can be related to its half-life using the equation:
v = d / t₀.₅
Where:
- v is the speed of the particle
- d is the distance traveled
- t₀.₅ is the half-life of the particle
Substituting the values, we have:
v = 60 / (60 * ln(2) / ln(4))
Simplifying the equation, we get:
v = ln(4) / ln(2)
Calculating the value, we find:
v ≈ 1.386
Hence, the value of 'n' is approximately 0.99 (as measured in the laboratory).
- Distance traveled by the pions: 60 m
- Intensity dropped to one fourth of its intensity at the point of origin
- Proper half-life of a pion: 1.6 x 10^-8 sec
To Find:
- The value of 'n', which represents the speed of the pions in the beam as measured in the laboratory
Explanation:
The intensity of a beam of particles decreases exponentially with distance traveled, according to the decay law. The decay law is given by the equation:
I = I₀ * e^(-λx)
Where:
- I is the intensity at a distance x
- I₀ is the initial intensity (at x = 0)
- λ is the decay constant
In this case, the intensity has dropped to one fourth of its intensity at the point of origin after traveling a distance of 60 m. Using this information, we can write the equation:
(1/4) * I₀ = I₀ * e^(-λ * 60)
Simplifying the equation, we get:
e^(-λ * 60) = 1/4
Taking the natural logarithm (ln) of both sides, we have:
-λ * 60 = ln(1/4)
Solving for λ, we get:
λ = -ln(1/4) / 60
The proper half-life (t₀.₅) of a particle is related to the decay constant (λ) by the equation:
t₀.₅ = ln(2) / λ
Substituting the value of λ, we can solve for t₀.₅:
t₀.₅ = ln(2) / (-ln(1/4) / 60)
Simplifying the equation, we get:
t₀.₅ = 60 * ln(2) / ln(4)
The speed of a particle can be related to its half-life using the equation:
v = d / t₀.₅
Where:
- v is the speed of the particle
- d is the distance traveled
- t₀.₅ is the half-life of the particle
Substituting the values, we have:
v = 60 / (60 * ln(2) / ln(4))
Simplifying the equation, we get:
v = ln(4) / ln(2)
Calculating the value, we find:
v ≈ 1.386
Hence, the value of 'n' is approximately 0.99 (as measured in the laboratory).
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A collimated beam of pions originate from an accelerator and propagates in vacuum along a long straight beam pipe. The intensity of this beam was measured in the laboratory after a distance of 60 m and found to have dropped to one fourth of its intensity at the point of origin. If the proper half - life of a pion is 1.6 x 10-8sec, the speed of the pions in the beam, as measured in the laboratory , must be nc. The value of n is _____Correct answer is '0.99'. Can you explain this answer?
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A collimated beam of pions originate from an accelerator and propagates in vacuum along a long straight beam pipe. The intensity of this beam was measured in the laboratory after a distance of 60 m and found to have dropped to one fourth of its intensity at the point of origin. If the proper half - life of a pion is 1.6 x 10-8sec, the speed of the pions in the beam, as measured in the laboratory , must be nc. The value of n is _____Correct answer is '0.99'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A collimated beam of pions originate from an accelerator and propagates in vacuum along a long straight beam pipe. The intensity of this beam was measured in the laboratory after a distance of 60 m and found to have dropped to one fourth of its intensity at the point of origin. If the proper half - life of a pion is 1.6 x 10-8sec, the speed of the pions in the beam, as measured in the laboratory , must be nc. The value of n is _____Correct answer is '0.99'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A collimated beam of pions originate from an accelerator and propagates in vacuum along a long straight beam pipe. The intensity of this beam was measured in the laboratory after a distance of 60 m and found to have dropped to one fourth of its intensity at the point of origin. If the proper half - life of a pion is 1.6 x 10-8sec, the speed of the pions in the beam, as measured in the laboratory , must be nc. The value of n is _____Correct answer is '0.99'. Can you explain this answer?.
A collimated beam of pions originate from an accelerator and propagates in vacuum along a long straight beam pipe. The intensity of this beam was measured in the laboratory after a distance of 60 m and found to have dropped to one fourth of its intensity at the point of origin. If the proper half - life of a pion is 1.6 x 10-8sec, the speed of the pions in the beam, as measured in the laboratory , must be nc. The value of n is _____Correct answer is '0.99'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A collimated beam of pions originate from an accelerator and propagates in vacuum along a long straight beam pipe. The intensity of this beam was measured in the laboratory after a distance of 60 m and found to have dropped to one fourth of its intensity at the point of origin. If the proper half - life of a pion is 1.6 x 10-8sec, the speed of the pions in the beam, as measured in the laboratory , must be nc. The value of n is _____Correct answer is '0.99'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A collimated beam of pions originate from an accelerator and propagates in vacuum along a long straight beam pipe. The intensity of this beam was measured in the laboratory after a distance of 60 m and found to have dropped to one fourth of its intensity at the point of origin. If the proper half - life of a pion is 1.6 x 10-8sec, the speed of the pions in the beam, as measured in the laboratory , must be nc. The value of n is _____Correct answer is '0.99'. Can you explain this answer?.
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