The kinetic energy of the Li++ ion is 11600 eV. The potential energy of the two protons is 9 x 10^9 eV. The kinetic energy of the ball is 1.61 x 10^19 eV.
Step-by-step explanation:
The kinetic energy of a Li++ ion that has accelerated from rest through a potential difference of 5800 V can be calculated using the formula KE = qV, where q is the charge of the ion (2e) and V is the potential difference (5800 V). Converting the answer to electron volts, we have KE = (2e)(5800 V) = 11600 eV. Therefore, the kinetic energy of the Li++ ion is 11600 eV.
The potential energy of two protons 8.0 fm apart can be calculated using the formula PE = kQ1Q2/r, where k is the electrostatic constant (9 x 10^9 Nm²/C²), Q1 and Q2 are the charges of the protons (+e), and r is the distance between them (8.0 fm = 8.0 x 10^-15 m). Converting the answer to electron volts, we have PE = (9 x 10^9 Nm²/C²)(e)(e)/(8.0 x 10^-15 m) = 9 x 10^9 eV. Therefore, the potential energy of the two protons is 9 x 10^9 eV.
To calculate the kinetic energy of a 220 g ball dropped from a height of 1.2 m, we can use the formula KE = mgh, where m is the mass of the ball (220 g = 0.220 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height (1.2 m). Converting the answer to electron volts, we have KE = (0.220 kg)(9.8 m/s²)(1.2 m) = 2.57 J = 2.57 Nm = 2.57 C·V. Since 1 eV is equal to 1.6 x 10^-19 J, the kinetic energy of the ball is (2.57 C·V) / (1.6 x 10^-19 C·V/eV) = 1.61 x 10^19 eV. Therefore, the kinetic energy of the ball is 1.61 x 10^19 eV.
The probable question can be: Express in eV (or keV or MeV if more appropriate): The kinetic energy of a Li^++ ion that has accelerated from rest through a potential difference of 5800 V. Express your answer to two significant figures and include the appropriate units. The potential energy of two protons 8.0 fm apart. Express your answer to two significant figures and include the appropriate units. The kinetic energy, just before impact, of a 220 g ball dropped from a height of 1.2 m. Express your answer to two significant figures and include the appropriate units.