Explanation: Given The wave function for the electron in one dimensional system is, Ψ ( x ) = sin x The probability density curve for the function Ψ 2 ( x ) = sin 2 x contains all the positive values of the given function over the whole range. Therefore, the probability density curve for the given function is, Figure 1 (b) Explanation: Given The wave function for the electron in one dimensional system is, Ψ ( x ) = sin x The probability of finding electron for the given function is maximum on the values of x where the probability density curve has the maximum value. For the given function the value of sin x is maximum at the values x = π 2 and x = 3 π 2 . Therefore, the probability density curve for the given function has a peak at these values of x where probability of finding an electron is maximum. (c) Explanation: The wave function for the electron in one dimensional system is, Ψ ( x ) = sin x The probability of finding electron for the given function is minimum on the values of x where the probability density curve has the minimum value. For the given function the value of sin x is zero at the value of x = π . Therefore, the probability density curve for the given function has a node at this value of x where probability of finding electron is nil. Conclusion: (a) The probability density curve for the given function is as follows: (b) The values of x is maximum at x = π 2 and x = 3 π 2 . (c) The probability of finding an electron at x = π is zero and this point is called node.
Explanation: Given The wave function for the electron in one dimensional system is, Ψ ( x ) = sin x The probability density curve for the function Ψ 2 ( x ) = sin 2 x contains all the positive values of the given function over the whole range. Therefore, the probability density curve for the given function is, Figure 1 (b) Explanation: Given The wave function for the electron in one dimensional system is, Ψ ( x ) = sin x The probability of finding electron for the given function is maximum on the values of x where the probability density curve has the maximum value. For the given function the value of sin x is maximum at the values x = π 2 and x = 3 π 2 . Therefore, the probability density curve for the given function has a peak at these values of x where probability of finding an electron is maximum. (c) Explanation: The wave function for the electron in one dimensional system is, Ψ ( x ) = sin x The probability of finding electron for the given function is minimum on the values of x where the probability density curve has the minimum value. For the given function the value of sin x is zero at the value of x = π . Therefore, the probability density curve for the given function has a node at this value of x where probability of finding electron is nil. Conclusion: (a) The probability density curve for the given function is as follows: (b) The values of x is maximum at x = π 2 and x = 3 π 2 . (c) The probability of finding an electron at x = π is zero and this point is called node.
Given The wave function for the electron in one dimensional system is,
Ψ(x)=sinx
The probability density curve for the function Ψ2(x)=sin2x contains all the positive values of the given function over the whole range. Therefore, the probability density curve for the given function is,
Figure 1
(b)
Explanation:
Given The wave function for the electron in one dimensional system is,
Ψ(x)=sinx
The probability of finding electron for the given function is maximum on the values of x where the probability density curve has the maximum value. For the given function the value of sinx is maximum at the values x=π2 and x=3π2 . Therefore, the probability density curve for the given function has a peak at these values of x where probability of finding an electron is maximum.
(c)
Explanation: The wave function for the electron in one dimensional system is,
Ψ(x)=sinx
The probability of finding electron for the given function is minimum on the values of x where the probability density curve has the minimum value. For the given function the value of sinx is zero at the value of x=π . Therefore, the probability density curve for the given function has a node at this value of x where probability of finding electron is nil.
Conclusion:
(a) The probability density curve for the given function is as follows:
(b) The values of x is maximum at x=π2 and x=3π2 . (c) The probability of finding an electron at x=π is zero and this point is called node.
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