16. Electron in a CRT In a cathode-ray tube (CRT) an electron is accelerated in

Question

16. Electron in a CRT In a cathode-ray tube (CRT) an electron is accelerated in a "gun" by allowing it to cross a region olinge oenial he acelesaig (a) Suppose V 25,000 V. Find the kinetic energy of the electron in joules. (b) Find the speed of the electron in m/s. (c) Suppose the same accelerating voltage was used with a proton instead of an electron. Give the answers to the same two questions [(a) and (b)] in this case. Explain. Note: The gun polarity would have to be reversed when launching a proton, but you don't need to take that into account in your calculations.

Explanation / Answer

If an electron is accelerated through a potential difference V, then kinetic energy is eV or electron volt.

So kinetic energy =eV=25000e

Kinetic energy in joules.

One eV=1.6 10^-19 joule.

So 25000eV=25000*1.6*10^-19 joules.

= 40*10^-16

=4*10^-15 joules.

As kinetic energy can be found by other formula which is

K. E=1/2mv² where m=mass(9.1*10^-31kg) and v=velocity.

Equating with the above relation

1/2mv²=eV

1/2*9.1*10^-31*v²=1.6*10^-19*25000

v²=1.6*10^-19*25000*2/9.1*10^-31

v²=1.6*25*10^15

v²=4*10^16

v=2*10^8 m/s. Ia the speed of electron.

For proton, since charge is same as that of electron

We have

K.E=qV

K.E=eV=25000e

One eV=1.6*10^-19 joules, so total K.E=

4*10^-15 joules.

B) ; as by above relation we have

K.E=1/2mv²=4*10^-15 joules

1/2 *1.67*10^-27*v²=4*10^-15

v²=4*10^-15*2/1.67*10^-27

v²=8*10^12/1.67

v²=4.8*10^12

v=2.19*10^6 m/s is the speed of proton. As the mass of the proton is much more than that of an electron, therefore its speed is very less as compared to an electron even after applying the same potential difference.

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