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A certain excited state of hydrogen atom is known to have a life of 2.5 × 10^{–14} s. The minimum error, with which the energy of the excited state can be measured is.
The energy time uncertainty relation is
The correct answer is: 0.026 eV
Which of the following is the eigenfunction of the linear momentum operator with a positive eigenvalue
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is the eigenvalue
The correct answer is: e^{ikx}
An eigenfunction of an operator The corresponding eigenvalue is.
The correct answer is: α^{2}
The ground state energy of an electron confined to a box 1Å wide is.
a = 1 * 10^{10}m m = 9.1 * 10^{31}kg
Energy of electron in ground state
E_{1} = h^{2}/8ma^{2}
⇒ [(6.625 * 10^{34})^{2}]/(8 * 9.1 * 10^{31} * 1 * 10^{10})^{2}
E_{1} = 6.016 * 10^{18} J
Which of the following values of A will properly normalize the wave function of a rigid dumbbell rotating about its centre having φ dependence as ψ(φ) = Ae^{imφ} where m is a quantum number.
For normalization
The correct answer is:
A particle of mass m has the wave function ψ(x, t) = e^{iωt} (α cos kx + β sin kx) where α, β are complex constants and ω and k are real constants. The probability current density is equal to :
Probability current density
subtract (2) and (1)
If deBroglie wavelength of an electron is 7.3Å. Then the velocity of electron is. Given, m_{e} = 9.1 × 10^{–31} kg and h = 6.6 × 10^{–34} Js.
Λ = h/mv
v = h/mΛ
v = (6.6*10^{34})/(9.1 × 10^{–31 }* 7.3 * 10^{10})
= 9.93 × 10^{4} m/s
The correct answer is: 9.93 × 10^{4} m/s
Which of the following is correct set of eigenvalues of the Hermitian matrix
The correct answer is: 1, 3
If ψ is a normalized solution of the Schrödinger equation and Q is the operator corresponding to a physical quantity x, then the quantity may be integrated in order to obtain :
The correct answer is: mean value of x
A particle limited to the x–axis has the wave frequency ψ = ax between x = 0 and x = 1, ψ = 0 elsewhere. The expectation value of the particle's position is.
The correct answer is: a^{2}/4
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