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16.Which of the following statements are correct? (A)If electrons have been accelerated from rest through a potential difference of 54 V, then the wavelength of electrons is 1.667 nm. (B)For high principle quantum number (n) for hydrogen atom, the spacing between the neighboring energy levels is proportional to 1/n³. (C)A particle of mass mₑ trapped in an infinite depth well of width L=1 nm. The transition from excited state n=2 to ground state n=1. The wavelength of light emitted is 886.4 nm. (D)The relation for total energy E and momentum p for a relativistic particle is E²=c²p²+m²c⁴. The product of group velocity and the phase velocity is equal to c². (E)If the electron wave function is Ce^(ikx) between x=2 and x=22 cm, zero everywhere else. The probability of finding the electron between x=0 and x=4 cm is 0.1.

15.Consider the Schrödinger Equation for the time-dependent state vector ψ(x,t) of a system. Which of the following statements are true? (A)A complete solution is given by ψ(x,t)=φE(x). (B)A complete solution is given by ψ(x,t)=φE(x)exp(iEt/ℏ). (C)The full solution can be written as a product c(t)φE(x), where c(t) is some complex function of time. (D)The function c(t) above can have any arbitrary functional form. (E)If measured at some future time, the energy of the system described by c(t)φE(x) is E.

14.Which of the following are true for electrons? (A)The same quantum state cannot be occupied by more than one electron. (B)Two electrons can have the same spin state. (C)At any temperature, electrons in a solid cannot be found above the Fermi level EF. (D)The existence of energy gap in a semiconductor can be proved within quantum physics. (E)None of the above.

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