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Problem 4 Easy Difficulty

(II) ($a$) What is the approximate radius of a $^{112}_{48}$Cd nucleus? ($b$) Approximately what is the value of $A$ for a nucleus whose radius is 3.7 $\times$ 10$^{-15}$ m?

Answer

a. $5.8 \mathrm{fm}$
b. 29

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Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Zachary M.

Hope College

Meghan M.

McMaster University

Video Transcript

30.4 1st we want to find the Radius cabbie and 1 12 And then we want to figure out the approximate mass number for a nucleus that has a radius of 3.7 centimeters. And we use the same equation for both force. So we know that the approximate new radius of a nucleus is this constant. 1.2 centimeters. It's the cube root of the masked number, and so here the mass number is 112 have a so we get 5.8 centimeters. It's going to be the radius of our can be, um, 1 12 nucleus. And here we just sort of invert this for a It's going to be the nuclear radius divided by this constant huge. This gives us 29.3, which can't be fractional. So, rounding to the nearest integer, we get 29

Cornell University
Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Zachary M.

Hope College

Meghan M.

McMaster University