If the solar system shrank so that the sun were located just one centimeter from Earth, about how far away could you find the ne
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Answer:
The energy of an electron in the 8th shell is given by: -0.2125 eV
The number of subshells is: 8
The number of orbitals is: 64
The number of electrons that fit on this shell is: 128
Explanation:
First, we find the energy of the electrons in the 8th shell. In order to do this, we recall that the energy of an electron (in the Hydrogen atom) whose principal number is n is given by:
Substituting n=8, we find that the energy is given by:
In order to find the number of subshells we recall that, for a given principal quantum number n, the possible values of the quantum number l, which corresponds to the number of subshells are:
0, 1, 2, ... , n-1
Since n = 8 in our problem, the possible values of l are: 0, 1, 2, 3, 4, 5, 6, 7. Therefore, the number of subshells are 8.
Now we continue with the number of orbitals. For every subshell l, we have 2l+1 possible values of m, which correspond to the orbitals. Since the possible values of l are: 0,1,2,3,4,5,6,7, therefore, we have to perform the sum:
And we can conclude that the number of orbitals is equal to 64.
Finally, we know that we can fit two electrons per orbital, therefore we can have 64*2 = 128 electrons in the shell corresponding to n=8.
Answer:
Work done, W = 6 J
Explanation:
It is given that,
Force of gravity acting on the book, weight of the book is 15 N
We need to find the work done in lifting the book straight up for a distance of 0.4 meters.
The weight of the book is acting in downward direction and the book is lifted straight up, it means angle between them is 180 degrees. Work done is given by :
So, the magnitude of work done in lifting the book is 6 joules.
a. I've attached a plot of the surface. Each face is parameterized by
• with
and
;
• with
and
;
• with
and
;
• with
and
; and
• with
and
.
b. Assuming you want outward flux, first compute the outward-facing normal vectors for each face.
Then integrate the dot product of <em>f</em> with each normal vector over the corresponding face.
c. You can get the total flux by summing all the fluxes found in part b; you end up with 42π - 56/3.
Alternatively, since <em>S</em> is closed, we can find the total flux by applying the divergence theorem.
where <em>R</em> is the interior of <em>S</em>. We have
The integral is easily computed in cylindrical coordinates:
as expected.