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(a) Assuming nuclei are spherical in shape, show that its radius $r$ is proportional to the cube root of mass number $(A) .$ (b) In general, the radius of a nucleus is given by $r=r_{0} A^{1 / 3},$ where $r_{0}$ is a proportionality constant given by $1.2 \times 10^{-15} \mathrm{m} .$ Calculate the volume of the $_{3}^{2} L$ i nucleus. (c) Given that the radius of a Li atom is $152 \mathrm{pm},$ calculate the fraction of the atom's volume occupied by the nucleus. Does your result support Rutherford's model of an atom?

(a) $r \propto \sqrt[3]{m}$(b) $\mathrm{V}=5.1 \cdot 10^{-44} \mathrm{m}^{3}$(c) $3.5 \cdot 10^{-13} \% ;$ the result supports Rutherford's model.

Chemistry 101

Chapter 2

Atoms, Molecules, and Ions

Atoms, Molecules and Ions

Carleton College

University of Central Florida

Drexel University

Lectures

18:42

(a) Assuming nuclei are sp…

02:22

01:43

01:26

06:16

(a) Describe Rutherford&#x…

Okay. First made. I work on part A off this question remembers of former laugh War. Morning, wolf. A sphere is the goes to four Overstreet Hyatt arm to the third. So we can say that William is dependent. Um, the Reedus, right. If we increase the radius on, the volume will be increased. Therefore, we can see that William is proportional to radius you. And we also know that the nucleus contains protons and Newhouse spread. So the volume off nucleus is proportional to the member off protons. And, um, you transit contains, which is the last member, Reg. So the volume off nucleus is proportional. True, The last number when we combine these two equations we don't mass is proportional, um, to the Reedus. So if we take the cube root off both sides, it gives us radius is proportional to the cube root of Samast number. Next, we are asked to calculate the volume off the new case of Leave them, Reg. So the volume, the phony laughter William just in the right again. So we just need to find out what's the reed? It's It's right. So the question gives us a somehow that we can use for the Reedus. Erling is just a constant and a ace the top of the mast number. Right? So, uh, this question asked us to a friend's outs and nucleus off lead, and we have the mass number off seven. So just plucking the mast number, we have the radius as two points three times 10 to the negative fifteens Nature now, using the volume from last week calculates be misuse as 5.1 times 10 to the negative, 40 of work cubic meter. So we just caught the volume off the leavin Lucas. Now we were asked to calculates a fraction off phantoms volume occupied by the new kits. To do that, we need to find out the actions. The listen items smaller, right? So the radiance off the listen item is 1:52 p.m. as convert eight in two meters one key and because, sure, 10 inches inactive transmitter. And I'm so 1 52 PM is 1.52 tensed inches. An active chance, major. Okay, now we can calculates a volume off a baby And me, you goes to four or three. Parents of this were hurt to the third and just party than under normally. On this 1.47 times, 10 to 29 killed a major. So finally we can calculate the fraction off. At times, Volume occupied has no place. It's just have plunged. Wound Constant was inactive. What Before your big meter, which is the volume off Salukis? We just did right the magic by the volume off the lesion, actually. So the ratio is like 3.5 times 10. Choose an active fifteens and if we are going to convert it into percentage, hence the 100 is 3 25 comes time to the 19 thirties percent, So the results are off course supports the Rutherford's model because he predicts that most of the atom is taking is like empty space, right? So the nucleus is only sweet 15 times into the thirties, percent off the entire atom wish means the rest of atom is empty.

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