The electron beam in a television tube consist of electrons accelerated from rest through a potential difference of about 20000v. What is the speed of the electrons?(ignore relativistic effects). Electron rest mass is 9.11/times10^(-31)kg and electronic charge is 1.6/ times10(-19) c (a)8.4/times10^(7)m/s(b)3.8/times10^(6)m/s(c)6/times10^(6)m/s(d)4.7/times10^(7)m/s
(b) 3.8*10^6 m/s
To find the speed of the electrons, we can use the equation for the kinetic energy of a particle:
KE = (1/2)mv²
Where KE is the kinetic energy, m is the mass of the electron, and v is its velocity.
Since the electrons are accelerated through a potential difference of 20000V, we can use the potential energy equation:
PE = qV
Where PE is the potential energy, q is the charge of the electron, and V is the potential difference.
The potential energy gained by the electron is equal to its kinetic energy, so we can equate the two equations:
(1/2)mv² = qV
Solving for the velocity v:
v = √(2qV / m)
Substituting the given values:
m = 9.11 x 10^(-31) kg
q = 1.6 x 10^(-19) C
V = 20000 V
v = √(2(1.6 x 10^(-19) C)(20000 V) / (9.11 x 10^(-31) kg))
v ≈ 8.4 x 10^7 m/s
Therefore, the speed of the electrons is approximately 8.4 x 10^7 m/s.
So, the correct answer is (a) 8.4 x 10^7 m/s.