I'm trying to make sense of this expansion. What is it and why. don't they do a mclaurin series expansion? If it is possible please do the Mclaurin expanision. If not just an explination. Thanks! Because of how large n is, it's necessary to rewrite the expression in square brackets.11G²M²m³2ħ²[n² (1-1)² n²ΔΕ ΞG²M²m³ 12ħ² n²G² M²m2ħ²n²G² M²m³23(²¹ ²m³ [1 + (-2) (-) + (-²)X-2 -¹) (-1)² + (-²)(-²-1)(-2²-²2 (-²) + -](-2)(-2-1)2ħ²n²2!3!2ħ²n²-2[(₁ - 1)^²-1]1--n234----][2 ( ₁² ) + 3 ( ² ) ² + 4 (¹) ²³ + 5 ( ²1 ) *1www.stemjock.comTherefore,Zn²Griffiths Quantum Mechanics 3e: Problem 4.20ΔΕ =The higher-order terms are extremely negligible compared to the first in the square brackets.G² M²m² [2 (²)]2ħ²n²G²M²mħ²GMh.= √√√ √²+(27) (1)ħ 1G²M²m² (Gm³ Mr.) (mg /GMr.)(1ħ²≈(1.054571726 × 10-34 J·s)(6.673 × 10-11 N.m²) (1.99 × 10³⁰ kg)(1.496 x 1011 m)³Page 6 of 6AE≈ 2.10 x 10-4¹ J.(3)

Answered: I'm trying to make sense of this…

I'm trying to make sense of this expansion. What is it and why. don't they do a mclaurin series expansion? If it is possible please do the Mclaurin expanision. If not just an explination. Thanks

Related questions

Q: Create a sketch of the observed solar emission (solar flux) as a function of wavelength. Your sketch…

A: THE VALUE PROVIDED IN THE QUESTIONS ARE AS FOLLOWS- A BLACKBODY WHICH START HEATING AND EMIT…

Q: 5. 그림의 두 도선은 d=10.0 cm 의 간격을 두고 떨어져 있고 각각이 I=5.00 A 의 반대 방향으로 흐르는 전류를 가진다. 두 도선의 중간지점에서 전체 자가장의 크기와…

A: Magnetic field at the midpoint between the wires…

Q: What is the total charge of all electrons in 18 /100 gram of Carbon dioxide CO2 ga: Your Answer:…

A: Given, Mass, m=0.18gramm=0.18×10-3kg The molecular mass of CO2, M=44g/mol Mole number,…

Q: You move your outdoor plant (where it is growing with full sun conditions - receiving all…

A: The rate of photosynthesis is defined as the measure of the rate at which radiant energy is being…

Q: In the deep space between galaxies, the density of atoms is as low as 106 atoms/m3, and the…

A: To determine,Part aThe pressure in the Pa.part bWhat volume (in m3) is occupied by 5 mol of gas.part…

Q: 2. Using your average Hubble's constant, calculate the age of the Universe. For this, first, we use…

A: Given: Hubble constant H=71 [km/sMparsec] According to Hubble`s law, it was found that the galaxies…

Q: the number of air density in a childs balloon is roughly the same as sea level air, 10^19 particles/…

A: Given: Here, n1 and n2 are the number densities. d1 and d2 are the diameters of the balloon.

Q: Cluster size and volume are not directly related. Explain how they are different. In the finite…

Q: Calculate the condensation temperature for liquid helium-4, pretending that the liquid is a gas of…

A: Given that density of liquid helium-4 is 0.145 g/cm3 We have to calculate the condensation…

Q: Do we expect to be able to use Maxwell–Boltzmann statistics to analyze: nitrogen gas at standard…

Q: MasteringPhysics: HW07 bMy Questions bartleby X X C G…

A: Given:Centripital acceleration of the ball just before it goes into free fall = 2gRadius of the…

Q: A wire in the shape of a rectangular loop of dimensions a=2m and b=lm moves with a constant velocity…

A: Given,a=2mb=1mv=10 m/sI=10AR=5 ohmr=20m

Q: 서양의 단위는 요을 사용한다. A conducting wire with a uniform radius of 0.40 cm and a length of 3.2 m is…

A: Given: radius r=0.40 cm length l= 3.2 m voltage V= 12 v current I=0.40 A

Q: What is a system and what is the universe, and how are they related to the 2nd Law of…

A: The thermodynamical state of a system can be defined with the help of the thermodynamic coordinates…

Q: I can't see the solution for step 2, it seems that it's missing. Can you repost the solution plea

A: Given, Initial internal diameter, di=50×10-3m Final internal diameter, df=50.05×10-3m Initial…

Q: 2. This is a schematic of a Geiger Counter. These are the things that go "clickety-click" when…

A: Gauss' law states that the the total electric field flux outside a volume is directly proportional…

Q: Star A has a temperature of 5,000 K and Star B has temperature of 6,000 K. At what wavelengths (in…

A: Temperature of star A = 5000 k temperature of star B = 6000 k

Q: In the deep space between galaxies, the number density of atoms is as low as 106 atoms/m3, and the…

Q: In the deep space between galaxies, the density of atoms is 1 million atoms per m3 (i.e. there are 1…

A: Given: Density of an atom = 1 million atom in a m3. Temperature = 3 K

Q: A muon is moving 12 m/s south when it experiences a constant acceleration of 7 m/s2 north. During…

A: The initial velocity of the muon, u=-12 m/s The constant acceleration, a=7 m/s2 Displacement,…

Q: 1. The mass of the Sun is about 2x1030 kg. The Sun was about 72% hydrogen when it first formed.…

A: Mass of the Sun, ms = 2x1030kg Initial amount of hydrogen in the Sun, Hi = 72% Amount of hydrogen…

Q: 4) Using the graphs given below, draw the following equations. Be sure to identify specific points…

Q: A planet has been discovered orbiting a K type main sequence star. A spectrum taken of this planet…

A: Given data : Wavelength of peak of the spectrum dpeak = 8.67×10-5cm = 8.67×10-7 m To find :…

Q: 16. You and a friend are sitting in the outfield bleachers of a major league baseball park, 140 m…

A: Given data The distance from the home plate to the field is D1 = 140 m The temperature of the…

Q: What are the properties of fourth matter Plasma?

A: During the ionization of atoms in a gas, plasma is formed, which conducts electricity evenly between…

Question

100%

I'm trying to make sense of this expansion. What is it and why. don't they do a mclaurin series expansion? If it is possible please do the Mclaurin expanision. If not just an explination. Thanks!

Because of how large n is, it's necessary to rewrite the expression in square brackets.
1
1
G²M²m³
2ħ²
[n² (1-1)² n²
ΔΕ Ξ
G²M²m³ 1
2ħ² n²
G² M²m
2ħ²n²
G² M²m³
2
3
(²¹ ²m³ [1 + (-2) (-) + (-²)X-2 -¹) (-1)² + (-²)(-²-1)(-2²-²2 (-²) + -]
(-2)(-2-1)
2ħ²n²
2!
3!
2ħ²n²
-2
[(₁ - 1)^²-1]
1--
n
2
3
4
----]
[2 ( ₁² ) + 3 ( ² ) ² + 4 (¹) ²³ + 5 ( ²1 ) *
1
www.stemjock.com
Therefore,
Zn²
Griffiths Quantum Mechanics 3e: Problem 4.20
ΔΕ =
The higher-order terms are extremely negligible compared to the first in the square brackets.
G² M²m² [2 (²)]
2ħ²n²
G²M²m
ħ²
GM
h.
= √√√ √²
+
(27) (1)
ħ 1
G²M²m² (Gm³ Mr.) (mg /GMr.)
(1
ħ²
≈(1.054571726 × 10-34 J·s)
(6.673 × 10-11 N.m²) (1.99 × 10³⁰ kg)
(1.496 x 1011 m)³
Page 6 of 6
AE≈ 2.10 x 10-4¹ J.
(3)

Expert Solution

Step 1

Given that the expression,we have

$∆ E = \frac{G^{2} M^{2} m_{E}^{3}}{2 h^{2}} [\frac{1}{n^{2} {(1 - \frac{1}{n})}^{2}} - \frac{1}{n^{2}}] = \frac{G^{2} M^{2} m_{E}^{3}}{2 h^{2} n^{2}} [\frac{1}{{(1 - \frac{1}{n})}^{2}} - 1] ∆ E = \frac{G^{2} M^{2} m_{E}^{3}}{2 h^{2} n^{2}} [{(1 - \frac{1}{n})}^{- 2} - 1] - - - - - - - - - - (1)$

Use the binomial expression,we have

${(1 + x)}^{n} = 1 + \frac{n x}{1!} + \frac{n (n - 1)}{2!} x^{2} + \frac{n (n - 1) (n - 2)}{3!} x^{3} + \frac{n (n - 1) (n - 2) (n - 3)}{4!} x^{4} . . . . . . . . . . . \infty h e r e |x| < 1$

Compare ${(1 - \frac{1}{n})}^{- 2}$ with ${(1 + x)}^{n}$

Here, $x = - \frac{1}{n}, n = - 2$

Now,

${(1 - \frac{1}{n})}^{- 2} - 1 = 1 + \frac{(- 2)}{1!} (\frac{- 1}{n}) + \frac{(- 2) (- 2 - 1)}{2!} {(\frac{- 1}{n})}^{2} + \frac{(- 2) (- 2 - 1) (- 2 - 2)}{3!} {(\frac{- 1}{n})}^{3} + \frac{(- 2) (- 2 - 1) (- 2 - 2) (- 2 - 3)}{4!} {(\frac{- 1}{n})}^{4} . . . . . . . . . . - 1 = 1 + \frac{2}{n} + \frac{6}{2 n^{2}} + \frac{24}{6 n^{3}} + \frac{25}{5 n^{4}} . . . . . . . . . . - 1 = 1 + \frac{2}{n} + \frac{3}{n^{2}} + \frac{4}{n^{3}} + \frac{5}{n^{4}} . . . . . . . . . . . . . - 1$

Put this value in the equation (1)

$∆ E = \frac{G^{2} M^{2} m_{E}^{3}}{2 h^{2} n^{2}} [{(1 - \frac{1}{n})}^{- 2} - 1] = \frac{G^{2} M^{2} m_{E}^{3}}{2 h^{2} n^{2}} [1 + \frac{2}{n} + \frac{3}{n^{2}} + \frac{4}{n^{3}} + \frac{5}{n^{4}} . . . . . . . . . . . . . - 1] ∆ E = \frac{G^{2} M^{2} m_{E}^{3}}{2 h^{2} n^{2}} [2 (\frac{1}{n}) + 3 {(\frac{1}{n})}^{2} + 4 {(\frac{1}{n})}^{3} + 5 {(\frac{1}{n})}^{4} . . . . . . . . . . . . .]$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Natural gas (CH.) fuel relcases 50 MJ per kilogram of fuel combusted. The reaction is CH, + 20, CO2 + 2H;0 Calculate the energy released per kilogram of CO2 emitted. [Energy released is Eepe E, where Eris energy released per kilogram of fuel combusted, mf is mass of a kilogram-mole of fuel (CH.), and mr is mass of a kilogram-mole of carbon dioxide (CO2). The Molecular mass of an atom of carbon, hydrogen and oxygen are 12, 1 and 16 respectively.]
Describe the four phases of matter. Compare their external, observable properties. Compare the nature of the forces between atoms or molecules (or both) in the four different phases of matter.
Can you suggest a possible origin for the helium gas that is part of the Earth's atmosphere?
PLEASE ANSWER THE HIGHLIGHTED QUESTION IN THE IMAGE. PLEASE PROVIDE A SIMPLE ANSWER.
c) Derive the Schwarzschild criterion for the onset of convection in an ideal gas, namely d ln T d ln P 7-1 Y Explain all steps in your derivation, and justify any assumptions that you make. d) In a region of convective instability near the surface of a solar-type star of total mass M, the temperature and pressure are related approximately by the expression P KT5/2. Show that the temperature gradient for an ideal gas in hydrostatic = equilibrium in this convection zone is given by dT dr 2Gm(r)μ 5Rr² Further, assuming that the mass in the convection zone is small compared to M, show that at a depth h measured from the top of the convection zone, the temperature is approximately given by T = Ts + 2GMμ -h₂ 5RR² when his small compared to R, and Ts is the temperature at the top of the convection zone.