Question

Suppose we have a vacuum with two metal plates separated by 2 meters. One of the plates has a hole in it so that a charged particle coming from the other one can pass through into empty space. ;The plate with a hole is attached to a voltage source of 5,000,000 V and electrons and muons are introduced near the other plate at 0 V. What energies and velocities do the electrons and muons have when they pass through the hole

Answer 1

hello your question has a some missing information below is the missing information

An electron is one of the most fundamental particles in nature. It is everywhere, in all the matter we can see, and it is with electrons that light interacts when it is emitted, absorbed, or scattered in everyday matter. The electron has a more massive cousin called a muon, also with a charge of -1 e, but with a mass of 1.88x10-28 kg. The electron's mass is 9.11x10-31 kg. You can see why a muon is called a "heavy" electron. A muon is also unstable, and left alone at rest in a lab it will turn into an electron, kinetic energy, and two neutrinos with a lifetime of 2.20x10-6 s.

answer :

energy and velocity of Electron : 8*10^-13 J , < 3*10^8 m/s

energy and velocity of Muon : 8*10^-13 J, 9.22 * 10^7 m/s

Step-by-step explanation:

Determine the energies and velocities of the electrons and Muons when they pass through the hole

i) energy of electron = q1 * V -- ( 1 )

V ( voltage ) = 5 * 10^6 V

q1 ( charge on electron ) = 1.6 * 10^-19 C

back to equation 1 ; energy of electron = ( 1.6 * 10^-19 ) * 5 * 10^6

= 8*10^-13 J

ii) velocity of electron = 1/2 * Me *( Ve)^2

1/2 * Me *( Ve)^2 = 8*10^-13

∴Ve =
`\sqrt{(8*10^(-13) )/(9.11*10^(-31) )}` < 3*10^8 m/s

iii) energy of muon

= Eu = q*v = 8*10^-13 J

iv ) velocity of Muon =
`\sqrt{(8*10^(-13) )/(1.88*10^(-28) )}` = 9.22 * 10^7 m/s