Answer
$5\;\rm peaks$
Work Step by Step
For a particle in a one-dimensional potential well (such as the infinite square well), the number of peaks (or maxima) in the probability density $ P(x) = |\psi(x)|^2 $ corresponds to the quantum number $ n $.
General Rule:
In an infinite potential well, the wave function $ \psi(x) $ for the $ n $-th quantum state has $ n - 1 $ nodes (points where $ \psi(x) = 0 $), and the probability density $ P(x) = |\psi(x)|^2 $ has $ n $ peaks .
For $ n = 5 $:
- The wave function $ \psi(x) $ will have $ 4 $ nodes.
- The probability density $ P(x) = |\psi(x)|^2 $ will have 5 peaks .
Thus, for a particle in the $ n = 5 $ quantum state, the probability density $ P(x) $ will have 5 peaks.
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