If the density of a certain spherical atomic nucleus is 1.0 * 10¹⁴ g cm^-3 and its mass is 2.0 * 10^-23 g, what is its radius in cm? A) 3.6 * 10^-13 cm B) 2.0 *0 10^-37 cm C) 4.8 * 10^-38 cm D) 2.2 * 10^-19 cm E) None of these choices is correct.

Question

Quizplus · Accepted Answer

The formula for the volume of a sphere is V = (4/3)πr^3 and the formula for density is ρ = m/V where m is mass. Solving for V and plugging in the given mass and density, we get:
V = m/ρ = (2.0 x 10^-23 g) / (1.0 x 10^10 g/cm^3) = 2.0 x 10^-33 cm^3
Now we can solve for the radius using the formula for volume:
V = (4/3)πr^3
r = [V / ((4/3)π)]^(1/3) = [(2.0 x 10^-33 cm^3) / ((4/3)π)]^(1/3) ≈ 3.6 x 10^-13 cm or 3.6 femtometers.
Therefore, the best choice is A.

If the Density of a Certain Spherical Atomic Nucleus Is