For 82^208 Pb find (a) the net electrical charge of the nucleus, (b) the number of neutrons, (

For 82^208 Pb find (a) the net electrical charge of the...

Key Concepts

Atomic Number and Net Charge

In nuclear physics, the atomic number refers to the number of protons in the nucleus, which directly determines the net electrical charge of the nucleus since each proton carries a positive elementary charge. This concept is vital as the net charge is crucial for understanding the interactions of the nucleus with electrons and other charged particles.

Neutron Number Calculation

The number of neutrons in an atomic nucleus is found by subtracting the atomic number from the mass number. Neutrons, being neutral, do not affect the net charge but play a key role in the stability and binding energy of the nucleus, making this calculation fundamental in nuclear structure and isotopic identity.

Mass Number and Nucleon Count

The mass number, which is the sum of protons and neutrons in the nucleus, represents the total number of nucleons. This is an essential concept because it relates directly to the atomic mass of the element and is used in various calculations including nuclear binding energy and reaction dynamics.

Nuclear Radius Estimation

The approximate radius of a nucleus can be estimated using an empirical formula that relates the radius to the mass number, typically expressed as R = R?A^(1/3) where R? is a constant. This concept is important for understanding the spatial dimensions of nuclei and for modeling nuclear interactions and reactions.

Nuclear Density Calculation

Nuclear density is determined by dividing the mass of the nucleus by its volume. Given the approximate spherical shape and the radius estimated from empirical formulas, this calculation is crucial for studying the properties of nuclear matter and understanding how densely the nucleons are packed within the nucleus.

Transcript

00:01 Hello, and in this question here we're going to investigate the density of the nukes.

00:05 So, to do this, we will first look at a lead atom.

00:11 Now, we write a lead atom as this, where this bottom number here refers to number of protons, and this top number here corresponds to number of nucleons.

00:35 And nucleons are protons and neutrons.

00:50 You might see that this top number here is represented by a and this number here is represented by z.

01:00 So first of all, to determine the net charge of the nucleus, so the nucleus is made up of protons and neutrons.

01:10 And here we see that it is 82 protons.

01:14 So protons have a positive charge.

01:29 And neutrons are neutral.

01:37 So the neutrons are going to contribute to the overall charge of the nucleus.

01:43 So the charge will only come from the protons.

01:47 Each proton contributes a plus one charge.

01:52 So the total charge charge is 82 times the charge of a neutron.

02:12 Sorry, of a proton.

02:18 Now, we know experimentally that the charge of a proton is equal to, so the charge q of a proton is equal to 1 .6 times 10 to the minus 19 of a cou.

02:30 So this means the total charge capital q is equal to 82 times the charge of a single proton, which is equal to 1 .32 times 10 to the minus 17 coulons.

02:49 Now to determine the number of neutrons, well, we have so a number of neutrons.

02:57 We have this top number up here, which is the number of protons and neutrons.

03:07 And this bottom number here is the number of protons.

03:10 So we simply subtract the top number from the bottom number.

03:13 So in this case, it will be 208 minus 82.

03:17 So 208 minus 82.

03:21 And that is equal to 126 neutrons.

03:26 Now, the top number above, so part c, the top number above, is, number of nucleons and number of nucleons and that is just given by the top number and that is equal to 208...

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