A flash of lightning transfers
1.5 x 10^9 Joules of energy through a potential difference of 5.0 x 10^7 Volts between a cloud and the ground. Calculate the quantity of charge transferred in the lightning bolt.
How many electrons were transferred?
Does this get easier? I hope so.
q =Energy/Δφ = 1.5•10^9 /5•10^7 =30 C,
N =q/e = 30/1.6•10^-19 = 1.87•10^10.
To calculate the quantity of charge transferred in the lightning bolt, we can use the formula:
Q = ΔV * C
Where:
Q = Quantity of charge transferred
ΔV = Potential difference (in volts)
C = Capacitance (in Farads)
In this case, we are given the potential difference, but we do not have information about the capacitance. However, we can solve for the capacitance by using the formula:
C = Q / ΔV
To calculate the quantity of charge transferred, we need to find the capacitance of the system.
Since we do not have the capacitance value, we can make an assumption that the capacitance is one Farad (F) for simplification purposes.
Using the given potential difference (ΔV = 5.0 x 10^7 Volts) and assumed capacitance (C = 1 Farad), we can calculate the quantity of charge transferred (Q):
Q = (5.0 x 10^7 Volts) * (1 Farad)
Q = 5.0 x 10^7 Coulombs
Therefore, the quantity of charge transferred in the lightning bolt is 5.0 x 10^7 Coulombs.
Now, to calculate the number of electrons transferred, we need to know the charge of a single electron.
The charge of an electron is approximately 1.6 x 10^(-19) Coulombs.
To find the number of electrons transferred, we divide the quantity of charge transferred by the charge of a single electron:
Number of electrons = (Quantity of charge transferred) / (Charge of a single electron)
Number of electrons = (5.0 x 10^7 Coulombs) / (1.6 x 10^(-19) Coulombs)
By performing this calculation, we find that approximately 3.13 x 10^26 electrons were transferred in the lightning bolt.
So, the number of electrons transferred is approximately 3.13 x 10^26.