5. A tin nucleus has charge +50e. Find the potential V at a distance of 10-12 meters from the nucleus and the potential energy U of a proton at this position. The proton has charge
+e = 1.6 x 10-19 C
It is wrong answer
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To find the potential V at a distance of 10^-12 meters from the tin nucleus, we can use the formula for the electric potential due to a point charge:
V = k * (q / r),
where V is the potential, k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance.
In this case, the distance r is given as 10^-12 meters, and the charge q is +50e. Here, e represents the charge of an electron, e = 1.6 x 10^-19 C. Therefore, the charge of the tin nucleus is:
q = 50e = 50 * (1.6 x 10^-19 C).
Substituting these values into the formula, we can calculate the potential V:
V = (8.99 x 10^9 Nm^2/C^2) * (50 * 1.6 x 10^-19 C) / (10^-12 m).
Now, let's solve for V:
V = (8.99 x 10^9 Nm^2/C^2) * (80 x 10^-19 C) / (10^-12 m)
= (8.99 x 10^9 Nm^2/C^2) * (8 x 10^-7 C/m)
= 7.192 x 10^3 Nm/C.
Therefore, the potential at a distance of 10^-12 meters from the tin nucleus is 7.192 x 10^3 volts (V).
To find the potential energy U of a proton at this position, we can use the formula:
U = q * V,
where U is the potential energy, q is the charge, and V is the potential.
In this case, the charge q of the proton is +e, which is 1.6 x 10^-19 C, and the potential V is 7.192 x 10^3 V. Substituting these values into the formula, we can calculate the potential energy U:
U = (1.6 x 10^-19 C) * (7.192 x 10^3 V)
= 1.1488 x 10^-15 J.
Therefore, the potential energy of a proton at a distance of 10^-12 meters from the tin nucleus is 1.1488 x 10^-15 Joules (J).
V = k Q /r which is the potential energy of a charge of one coulomb at distance r from charge Q
V = (9*10^9)(50*1.6*10^-19) / 10^-12
U = q V = 1.6*10^-19 * V