A radioactive particle weighing 7.20 x 10³ ng is found 110 m above the earth's surface. What is its potential energy?

• A. 7.8 x 10^-6 J
• B. 7.2 x 10^-9 J
• C. 7.9 x 10^-9 J
• D. 7.2 x 10^-6 J

Answer: (A)

Verified step by step guidance

1. Convert the mass of the radioactive particle from nanograms (ng) to kilograms (kg) since the standard unit of mass in physics is kilograms. Use the conversion factor: 1 ng = 1 x 10^-12 kg.
2. Identify the height (h) above the Earth's surface, which is given as 110 meters.
3. Use the formula for gravitational potential energy: U = mgh, where U is the potential energy, m is the mass in kilograms, g is the acceleration due to gravity (approximately 9.81 m/s^2), and h is the height in meters.
4. Substitute the values for m, g, and h into the potential energy formula. Ensure that all units are consistent, particularly that mass is in kilograms and height is in meters.
5. Calculate the potential energy using the substituted values to find the answer in joules (J).