if electron are caused to fall through a potential difference of 100000 voltage , determine their final speed if they were initially at rest.
e*100,000 is the kinetic energy.
e is the electron charge,1.6*10^-19 C
Set 100,000*e equal to (1/2)mV^2 and solve for V
m is the electron mass.
Soon hkjd k cbz he me z zzz jbz
To determine the final speed of electrons when they fall through a potential difference of 100,000 volts, we need to use the formula for the kinetic energy (K.E.) of a charged particle:
K.E. = qV
Where:
K.E. is the kinetic energy gained by the particle,
q is the charge of the particle (electron, in this case),
V is the potential difference.
First, let's find the charge of an electron. The charge of an electron, denoted as 'e', is approximately -1.6 x 10^-19 coulombs.
Now, we can plug in the values into the formula:
K.E. = (-1.6 x 10^-19 C) * (100,000 V)
Calculating this multiplication, we get:
K.E. = -1.6 x 10^-19 C * 100,000 V
= -1.6 x 10^-14 J
Since the potential difference accelerates the electron, it gains kinetic energy. We can equate the kinetic energy gained to the initial kinetic energy of the electron at rest, assuming no energy loss due to resistance or other factors:
K.E. gained = 0.5mv^2
Where:
m is the mass of the electron,
v is the final speed of the electron.
To find the final speed, we rearrange the equation:
v^2 = (2 * K.E. gained) / m
Plugging in the values:
v^2 = (2 * (-1.6 x 10^-14 J)) / (9.1 x 10^-31 kg)
Now, we can calculate the final speed (v):
v^2 = -3.52 x 10^16 m^2/s^2
v = √(-3.52 x 10^16) m/s
Please note that the value obtained is imaginary because the kinetic energy gained by the electron cannot be negative. In actual practice, electrons would gain kinetic energy and have a final speed, but the above calculation neglects other factors involved, such as resistance and energy loss.
p.d.=100000V
therefore, workdone , W=q×p.d.
W=1.6×10^-19 × 100000
=1.6×10^-14 Joules
since work done = force × displacement
F×s=1.6×10^-14
m×a×s=1.6×10^-14
9.1×10^-31×a×s=1.6×10^-14
a×s=(1.6×10^-14)÷(9.1×10^-31)
a×s=1.75×10^17
v^2/2=1.75×10^17
v=5.09×10^8m/s
By deriving a formula ,from work energy theorem,we get:- V=√{2×e×v×}/m
Where,m=mass of electron
e=charge on an electron
v=potential difference
V=final velocity of an electron
Recall that one electron-volt is the energy gained by an electron in moving through a potential difference of 1 V, so
1 eV = 1.6 * 10^-19 Joules
1,000,000 V = 1.6 ^ 10^-19 * 10^6 Joules = 1.6 * 10^-13 J
So this must be the kinetic energy gained be the electron.
KE = (1/2) m v^2
From reference tables
mass of electron = 9.11 * 10^-31 kg
So
1.6 * 10^-13 = (1/2) * 9.11 * 10^-31 * v^2
v^2 = 2 * 1.6 * 10^-13 / 9.11 * 10^-31 = 0.35 * 10^18
v = 0.59 * 10^9 m/s