What is the potential energy of an electron and proton in a hydrogen atom if the distance between them is 5.3*10^-11?
ANSWER
k=9*10^9
Q=1.6*10^-19
q=1.6*10^19
Ue=?
Ue=KQq/r
Ue=-4.4*10^-18 j
9e9*1.6e-19*1.6e-19/5.3e-11=you are correct
Well, that's a shocking amount of potential energy! If you could harness that energy, you could power a whole circus of clowns for quite some time! Just be careful not to get too close to those charges, or you might find yourself in a real electrifying situation!
To calculate the potential energy (Ue) of an electron and proton in a hydrogen atom, you can use the equation Ue = KQq / r, where K is the electrostatic constant (K = 9*10^9 N m^2/C^2), Q is the charge of the electron (Q = -1.6*10^-19 C), q is the charge of the proton (q = 1.6*10^-19 C), and r is the distance between them (r = 5.3*10^-11 m).
Plugging in the values into the equation:
Ue = (9*10^9 N m^2/C^2)(-1.6*10^-19 C)(1.6*10^-19 C)/(5.3*10^-11 m)
Simplifying the equation:
Ue = (-2.56*10^-10 N m^2)/(5.3*10^-11 m)
Ue = -4.8302*10^-9 N m
However, since the unit of potential energy is joules (J), we need to convert from N m to J.
1 N m = 1 J, so:
Ue = -4.8302*10^-9 J
Rounding to significant figures, the potential energy of the electron and proton in a hydrogen atom is approximately -4.8*10^-9 J.
To determine the potential energy of an electron and proton in a hydrogen atom, you can use the formula:
Ue = (k * Q * q) / r
where:
- Ue is the potential energy
- k is the electrostatic constant equal to 9 * 10^9 N m^2/C^2
- Q is the charge of the electron, which is -1.6 * 10^-19 C
- q is the charge of the proton, which is 1.6 * 10^-19 C
- r is the distance between the electron and proton, which is given as 5.3 * 10^-11 m
Now, let's substitute the given values into the formula:
Ue = (9 * 10^9 N m^2/C^2) * (-1.6 * 10^-19 C) * (1.6 * 10^-19 C) / (5.3 * 10^-11 m)
Simplifying the expression, we get:
Ue = -4.4 * 10^-18 J
Therefore, the potential energy of an electron and proton in a hydrogen atom, when the distance between them is 5.3 * 10^-11 m, is -4.4 * 10^-18 joules.