How many times larger is the radius of the nucleus ²⁰⁸Pb (Z=82)compared to the nucleus ⁴⁰Ca (Z=20)? A)0.58 B)1.7 C)5.2 D)4.1 E)2.3

Question

Quizplus · Accepted Answer

The radius of a nucleus is given by the formula R= R0*A^(1/3), where R0 is a constant and A is the mass number of the nucleus. Since we are comparing two nuclei with different mass numbers, we need to use ratios to solve for the radius ratio.

For nucleus Pb, R(Pb) = R0 * 208^(1/3)
For nucleus Ca, R(Ca) = R0 * 40^(1/3)

Taking the ratio of these two equations, we get:

R(Pb)/R(Ca) = (R0 * 208^(1/3))/(R0 * 40^(1/3)) = (208/40)^(1/3) = 1.693

Therefore, the radius of the Pb nucleus is 1.693 times larger than the radius of the Ca nucleus.

The answer is B) 1.7.

How Many Times Larger Is the Radius of the Nucleus