Problem 6 Medium Difficulty

Consider the $^{65}_{29} \mathrm{Cm}$ nucleus. Find approximate values for its (a) radius, (b) volume, and (c) density.

Answer

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Video Transcript

in number six were asked to find the approximate radius volume and density of copper 65. I'm so radius, We're going to use my nuclear radius equation here. This is the constant proportionality. Um, this is the atomic mass raised to the 1/3 power. Well, this constant is 1.2 times 10 to the negative. 15 meters or 1.2 50 meters. But I'm going to keep it in that my atomic number 65? No, my atomic mass. No, my mass number is 65 you know, raise that the third power and I get 4.8 centimeters or 4.8 times 10. It's the negative 15th meters. Um, report be one of the volume. Well, I'm assuming it's spherical. So the volume of a sphere is 4/3 pi r cubed. And I just found our so 4/3 pie times 4.8 times 10 to the negative 15 meters. And like it's cute. I get it. She probably only have two significant figures on this. Also, I get 4.6 times 10 to the negative 43 with the meter's cubed and then for part C m finding density Well, densities and mass pavilion my mask. This mass number. That's how many atomic mass units. I'm going to change that to Kilograms. I'm gonna do that right in my equation here. So this is 65. They usually don't include units in here, but I'm going to 65. You and we have available conversion in here. Um, I looked it up and I know there's 1.66 times 10 to the 27th kilograms and each you So 1.66 times 10 to the negative. 27th. When that is kilograms. Kilograms. True. That's one Promise unit and then the bottom My volume is gonna be in this meters cubed soon. Tell Mei Yue's canceled and I'm left in kilograms per meter. Cute. I get 2.33 I guess I should just have 2662.3 times Tentatively 17 kilograms per meter. Cube. They're very dense.