A supersonic: - plane travels al . As this plane passes two markers a distance of apart on the ground, how will the time interval registered on a very precise clock onboard me plane differ from ?
The value of time difference in the plane’s clock is .
Consider a time difference is .
Consider a speed of the plane is .
Consider a distance is .
Write the formula of time difference in the plane’s clock.
Here, is time difference, speed of the plane and speed of light.
Due to relativistic effects, time relative to an object moves more quickly when it is moving very quickly. The time-dilation equation helps explain this:
Arrive at the following expression for the time difference in the plane's clock using the time-dilation equation:
Calculate the time difference in the clock of the aircraft using the formula for :
Determine the time difference in the plane’s clock.
Substitute for , for and for into equation (1).
According to the findings, the plane's clock would display the time earlier.
71. In many kinds of integrated circuits. the preferred element of amplification/switching is nor the bipolar transistor discussed in the chapter, but the MOSFET (metal oxide semiconductor field effect transistor). Thecompany diagram shows one in its "normally off" state: Conduction electrons cannot flow from the n-type source, which is analogous to the emitter. "over the bump" in the ptype region to the n-type drain. analogous to the collector. (Annpn arrangement is shown. but just as for the bipolar transistor, a pnp would yield the complementary device.) The important difference is that rather than a direct electrical contact to the p-type region, as in the base of the bipolar, the centre lead, the gate, is a conductor bonded to the p-type region but separated by a thin insulating layer.
(a) Explain how applying a bias to the gate can cause this device to tum on. Should the gate bias voltage be positive or negative (relative to the source)? Why is the control mechanism referred to as "field effect"?
(b) The MOSFET is often said to be a "unipolar" device because valence holes (conduction elections in the pnp device) do not play the important role that they do in the bipolar. Explain. Would you expect a significant current through the gate due to electron-hole recombination in the p-type region? Why or why not?
(c) A low-input-impedance device is one in which there are large oscillations in input current for small oscillations in the input voltage. Correspondingly, a highinput-impedance device has a small input currentfor a large input voltage. Bearing in mind that the voltage across the forward-biased base-emitter diode of a bipolar transistor is always about , while the input current is proportional to the output current, would you say that the bipolar transistor has low or high input impedance? What about the MOSFET?
The state –2p the state in which has most of its probability density along the z-axis, and so it is often referred to as a state. To allow its probability density to stick out in other ways and thus facilitate various kinds of molecular bonding with other atoms, an atomic electron may assume a wave function that is an algebraic combination of multiple wave functions open to it. One such “hybrid state” is the sum (Note: Because the Schrodinger equation is a linear differential equation, a sum of solutions with the same energy is a solution with that energy. Also, normalization constants may be ignored in the following questions.)
(a) Write this wave function and its probability density in terms of r, , and , (Use the Euler formula to simplify your result.)
(b) In which of the following ways does this state differ from its parts (i.e., and ) and from the 2pz state: Energy? Radial dependence of its probability density? Angular dependence of its probability density?
(c) This state is offer is often referred to as the . Why?
(d) How might we produce a state?
A function is nonzero only in the region of width centered at
where C is a constant.
(a) Find and plot versus the Fourier transform of this function.
(b) The function ) might represent a pulse occupying either finite distance (localid="1659781367200" position) or finite time (time). Comment on the wave number if is position and on the frequency spectrum if is time. Specifically address the dependence of the width of the spectrum on .
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