show that 1ev=1.6×10^-19J
Answers
Answer:
With three equations from physics we'll show the relationship between two units of energy: electron-volts (eV) and joules (J). These equations involve integration, vectors and dot products, but all we're interested in are the variables and, in particular, the units used to measure these variables.
The first equation says that the voltage, V, is equal to the negative of the integral of the electric field vector, E, dotted with the vector path element dl.
Edot_dl
The variables and their units are as follows:
Voltage, V: measured in volts [V]
Electric field, E: is measured in volts/meter [V/m]
Path element, dlL: has units of meters [m]
Note the shortened abbreviation for the units is written within brackets so as not to confuse these letters with the variables in the equations.
The second equation says the force vector, F, is equal to the product of the electric field vector, E, and the charge, q.
F=qE
The variables and their units are as follows:
Voltage, F: measured in newtons [N]
Electric field, E: In addition to the units [V/m], the electric field is also measured in newtons/coulombs [N/C]
Charge, q: has units of coulombs [C]
The third equation says the work, W, is equal to the integral of the force vector, F, dotted with the vector path element, dl.
W=Fdot_dl
The variables and their units are as follows:
Work, W: measured in joules [J]
Force, F: measured in newtons [N]
Path element, dl: has units of meters, [m]
Continuing to write the units with brackets, we can say:
From the first equation, the electric field, E, has units of [V/m].
Substituting into the second equation this [V/m] for E gives us [N] = [C] [V/m].
In the third equation, the work in joules is equal to the force in newtons times a distance in meters, giving us [J] = [N] [m].
Combining these units, we can see the changes as follows, with m eventually being cancelled out:
W=units_cancelling
One electron, e, has a charge of 1.6x10-19 coulombs.
Thus, because joules equals coulombs times voltage, we get:
W=conversion
Multiply both sides by 1.6x10-19 to get 1 eV = 1.6x10-19 J.
Explanation:
Answer:
The value of 1eV in terms of joules is 1.6 × 10⁻¹⁹ J.
Explanation:
Given,
1eV = 1 electronvolt
To find,
The value of 1eV in terms of Joules
Concept,
- The energy gained by an electron (a charged particle carrying unit electronic charge) when the electrical potential at the electron increases by one volt.
- Most commonly we use the unit eV in atomic and nuclear physics.
Calculation,
We know that the charge of the electron is e = 1.6 × 10⁻¹⁹ C....(1)
And 1 Coloumb Volt = 1 Joule....(2)
Hence, from equation (1)
1eV = 1.6 × 10⁻¹⁹ (CV)
Now from equation (2)
1eV = 1.6 × 10⁻¹⁹ J
Therefore, the value of 1eV in terms of joules is 1.6 × 10⁻¹⁹ J.
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