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For a system of two fermionic particles that can be in any one of three possible quantum states each, the ratio of the probability that two particles are in the same state to that when the two particles are in different states is
  • a)
    1
  • b)
    1/2
  • c)
    0
  • d)
    1/3
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
For a system of two fermionic particles that can be in any one of thre...

Explanation:

Probability of two particles in the same state:
- For the two particles to be in the same state, there are 3 ways it can happen (both in state 1, both in state 2, both in state 3).
- The probability of both particles being in the same state is given by (1/3) * (1/3) = 1/9.

Probability of two particles in different states:
- For the two particles to be in different states, there are 3 ways it can happen (particle 1 in state 1 and particle 2 in state 2, particle 1 in state 1 and particle 2 in state 3, particle 1 in state 2 and particle 2 in state 3).
- The probability of both particles being in different states is given by (1/3) * (2/3) = 2/9.

Ratio of probabilities:
- The ratio of the probability that two particles are in the same state to that when the two particles are in different states is (1/9) / (2/9) = 1/2.

Therefore, the correct answer is option C) 0, as the ratio of the probabilities is 1/2, not 0.
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Community Answer
For a system of two fermionic particles that can be in any one of thre...
  • For a system of two fermionic particles, the Pauli exclusion principle applies, which states that no two fermions can occupy the same quantum state simultaneously.
  • This means that the probability of finding two fermions in the same quantum state is zero.
  • Therefore, the ratio of the probability that two fermionic particles are in the same state to the probability that they are in different states is 0.
  • Since fermions cannot occupy the same state, the ratio doesn't have a well-defined value.
  • The probability of finding two fermions in the same state is zero, making the ratio undefined in this case.
Hence, the probability that two particles are in the same state to that when the two particles are in different states is 0.
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For a system of two fermionic particles that can be in any one of three possible quantum states each, the ratio of the probability that two particles are in the same state to that when the two particles are in different states isa)1b)1/2c)0d)1/3Correct answer is option 'C'. Can you explain this answer?
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