In a classic model, the electron of a hydrogen atom circles the proton at a radius of 0.0529·10−9m when it is in the n=1 state. What is its electric potential energy?
PE= Vq= kq/r * q where the first q is charge on proton, the second q is charge on electron
I still lost.
To calculate the electric potential energy of an electron in a hydrogen atom, you will need to use the formula:
Potential Energy = (-e^2) / (4πε₀r)
Where:
- "e" is the charge of an electron (-1.602 x 10^-19 C)
- "ε₀" is the permittivity of free space (8.854 x 10^-12 C^2/Nm^2)
- "r" is the radius of the electron's orbit around the proton (0.0529 x 10^-9 m)
Now, let's plug the values into the formula to calculate the electric potential energy:
Potential Energy = (-(-1.602 x 10^-19 C)^2) / (4π(8.854 x 10^-12 C^2/Nm^2)(0.0529 x 10^-9 m))
First, let's simplify the expression:
Potential Energy = (1.602 x 10^-19 C)^2 / (4π(8.854 x 10^-12 C^2/Nm^2)(0.0529 x 10^-9 m))
Next, let's calculate the numerator:
(1.602 x 10^-19 C)^2 = 2.571204 x 10^-38 C^2
Now, let's calculate the denominator:
4π(8.854 x 10^-12 C^2/Nm^2)(0.0529 x 10^-9 m) = 1.113×10^-20 C^2/Nm
Finally, divide the numerator by the denominator to get the electric potential energy:
Potential Energy ≈ 2.571204 x 10^-38 C^2 / 1.113 x 10^-20 C^2/Nm
Potential Energy ≈ 2.31 x 10^-18 J
Therefore, the electric potential energy of the electron in the n=1 state of a hydrogen atom is approximately 2.31 x 10^-18 Joules.