Electric Charge

An electron in the Coulomb field of a proton is in the following state of coherent superposition of orthonormal states :Let and represent the first three energy levels of the system. A sequence of measurements is done on the same system at different times. Energy is measured first at time and the outcome is . Then total angular momentum is measured at time , and finally, energy is measured again at . The probability of finding the system in a state with energy after the final measurement is . The value of is ______ (in integer).

A particle of mass in an infinite potential well of width is subjected to a perturbation as shown in the figure, where is Planck's constant.

The first-order energy shift of the fourth energy eigenstate due to this perturbation is . The value of is ____ (in integer).

The curves and schematically show the variation of X-ray intensity with wavelength at two different accelerating voltages for a given target material. In the figure, Å, Å, Å, and Å. Take Planck's constant as Js, the speed of light as m/s, and the elementary charge as C.

Which of the following statement is/are true?

Two point charges of charge each are placed a distance apart. A grounded solid conducting sphere of radius is placed midway between them. Assume . Which of the following statements is/are true?