Solid State Physics is also related to chemistry, possessing some of the remarkable properties of physical chemistry.
Physical chemistry is so annoying; physics students are afraid of it, and chemistry students are afraid of it too.
In fact, Shen Qi was also a little afraid of materialism. This thing was both material and material, yet neither material nor material; it could kill without consequence, but it was designed to kill you.
For this question, the total energy Ep of the interactions between ions in NaCl crystal has already been given.
When r deviates from r0, Ep deviates from Ep0, let the deviation be U.
Let x represent the relative offset. To obtain the power series relationship between U and x, we need to perform a Taylor expansion, that is, use the Taylor expansion of Ep at r0.
It's really torturous. To do a physics problem, you have to know Taylor expansion. Fortunately, Taylor expansion is very simple... Shen Qi started answering the questions on the test paper.
The power series expression for U(x) is:
U(x)=A0+A1x+A2x^2+A3x^3+...
From adiabatic compression, we know that:
1/κ=-V(dp/dV)∣r=r0
... d^2Ep/dV^2=d/dV(dEp/dr*dr/dV)=...
The final values are: m = 9.4; α = 1.77; am = 2.53 × 10^-109 J * m^9.4
I don't know if this is right or wrong, but this is the only way. Time is short, and there are still five questions left. Shen Qi quickly moved on to answering the remaining questions.
The fourth question seemed ordinary at first glance, but after careful consideration, Shen Qi realized, "Holy crap, it's terrifying!"
"A certain amount of Diethyl Ether is sealed in a glass tube, part of which is in a liquid state and the other part is in a gaseous state."
"If there are no other impurities in the tube, and the volume inside the tube is exactly the critical volume of these Diethyl Ether, then when slowly heated to the critical temperature, the liquid surface will disappear because the gas and liquid phases will no longer be different..."
Although the first three questions took up a lot of time, Shen Qi carefully reviewed the question again for the fourth question.
Upon reaching this point in the question, Shen Qi felt a sense of foreboding, and a chill ran down his spine.
It involves liquids, gases, and critical states...
What does this tell us?
What does this signify?
Van der Waals Gas!
Without a doubt, any question involving van der Waals gases is a pure physics and chemistry question.
What you fear most is what happens.
Is that it?
That's it!
It shouldn't have come.
But it has already arrived.
It did come after all.
Silence, a moment of silence.
Shen Qi must act in the shortest possible time.
Solve a problem.
Inside the glass tube.
The ratio of gas phase to liquid phase.
How much exactly?
Diethyl Ether is colorless and transparent.
However, it is a deadly liquid in the material world of martial arts.
Deadly liquid.
Murder is invisible.
Wherever van der Waals is, there is a world of its own.
But the most dangerous substance is not the liquid.
Rather, it is.
Gas and liquid coexist.
Bg and B1.
Finally, Shen Qi began to write:
Take 1 mol of Diethyl Ether. As the temperature changes, the total volume is Vk, and the mole fractions of the gas phase and liquid phase are α(T) and β(T), respectively.
αVg+βV1=Vk
When the temperature is T, the saturated vapor pressure is p0. Using the equal area method, we get:
∫<sub>upper</sub>Vg<sub>lower</sub>V1pdv=p<sub>0</sub>(Vg-V1)
Substituting into the integral, we get:
RTlnVg-b/V1-ba(1/V1-1/Vg)=p0(Vg-V1)
From the Van der Waals Equation:
ΨVan ΦΨ equation *Imagine swastika
Find:
Liquid phase B1 = 44.1%
Gas phase Bg = 55.9%
Ultimately, Shen Qi gave his answer: the ratio of liquid phase B1 to gas phase Bg.
I completed the first four questions, which took two hours.
With four questions remaining, Shen Qi only has one hour to answer them.
It's not that he didn't try; this national competition final exam was really difficult.
After completing questions 5, 6, and 7, Shen Qi only had 10 minutes left.
Just then, the contestant in front of Shen Qi finished tidying up his stationery and raised his hand.
Shen Qi was very familiar with this behavior; he used to do it often, handing in his papers early.
The proctor walked over to the student in front of Shen Qi and asked softly, "Have you handed in your paper?"
"Yes." The contestant nodded. He came from Hangzhou Second High School, a top-ranked school in the competitive physics field in Zhedong Province.
The student from Hangzhou Second High School was sitting right in front of Shen Qi, and Shen Qi couldn't ignore him even if he wanted to.
Whether it's math competitions or physics competitions, teachers and students involved in subject competitions have all heard of the great name of Hangzhou Second High School.
Although both are No. 2 Middle Schools, Shen Qi's Nangang Second High School cannot compare with Suzhou and Hangzhou Second High School. Hangzhou Second High School operates as a group with branches all over the place, while Nangang Second High School only has a few acres of land and is just entertaining itself.
"Take it or leave it, I'm tired of this kind of game." Shen Qi watched the students from Hangzhou Second High School hand in their papers and leave, then began to review the last question.
The last question is not easy; it takes several minutes just to read the question carefully.
"In a particle collision experiment, a slow-moving k- meson was observed to interact with a stationary proton p, producing a π+ meson and an unknown X particle."
"Given that the magnetic induction intensity of the magnetic field B is B = 1.70 Wb/m^2, the radius of curvature of the π+ meson track is measured to be R1 = 34.0 cm."
1. Determine the radius of curvature R2 of the track of X particle.
2. Please see the table below:
The table headers are: particle name, symbol, -rest mass/MeV+, and charge (e).
The specific information for each line is as follows:
Positron, electron; e+, e-; 0.511; ±1
Muon; μ+, μ-; 105.7; ±1
Pi+ Meson; π+, π-; 139.6; ±1
Neutron; n; 939.6; 0
Lambda Particle; Λ^0; 1115.4; 0
Negative Sigma- Particle; Σ-; 1197.2; -1
Neutral Ξ particle; Ξ^0; 1314.3; 0
..."
The particle list has more than a dozen rows.
The second question is, "What kind of particle is x?"
With 10 minutes allotted for reviewing the question and answering it, Shen Qi only had 10 minutes left.
For an average person, they would probably give up on solving the last question.
But Shen Qi did not give up. After carefully reviewing the question, he still had 7 minutes left.
This is a Modern Physics problem. The solution should be... what the hell do you need a solution for? The situation is critical in this emergency, let's just solve it on the test paper!
Without hesitation, Shen Qi picked up his pen and began writing.
Considering the Lorentz Force, the velocity magnitude and mass of the two particles remain constant.
Newton's second law in Theory of Relativity form:
F=d/dt(mv)
π+ mesons and X particle undergo circular motion under the influence of the Lorentz Force, with a radius of rotation of:
R=mv/eB
Since m1v1 = m2v2 and the absolute values of the charges of the two particles are the same, the radius R2 of the circular track of the particle is the same as the radius R1 of the circular track of the π+ meson.
Therefore, R2 = R1 = 34.0 cm
Shen Qi spent 3 minutes answering the first question: the radius of curvature R2 of the X particle track is the same as R1 of the π+ meson, both being 34.0 cm.
"My problem-solving speed is unmatched, faster than the speed of particles..." Shen Qi completed the first question with lightning speed.
There's no other way; people are forced to their limits. Adversity might unleash a level 15 fighting power.
What the hell? R2 equals R1? I don't even believe this answer myself... Shen Qi has no choice but to believe it. There are only 3 minutes left, and he must complete the second question immediately. There is no time to check the correctness of the first question.
The second question requires Shen Qi to determine what kind of particle x is.
Based on the radius of curvature of X particle calculated in the first question as R2=R1=34.0cm, Shen Qi needs to perform some calculations to determine what kind of particle x is.
If the answer to the first question is wrong, the answer to the second question will inevitably be wrong as well.
There's no going back, there's no time left.
Even if you get the first question wrong, you have to grit your teeth and keep going even if you're wrong!
This was Shen Xueba's last act of defiance.
Shen Qi once again unleashed his lightning-fast hand speed and powerful mathematical calculation ability, calculating directly on the test paper:
v1 = eBR1c / √m10^2c^2 + e^2B^2R1^2 = 1.6 × 10^-19 × 1.7 × 0.34 ×... m/s
Despite the tight schedule, Shen Qi still followed what he considered to be rigorous and correct steps for derivation and calculation. He made sure to write out all the formulas that needed to be written and included a few words to explain the key steps that required text, such as "substitute, get". This is a basic quality that a top student should possess.
Substituting, we get: m20c^2 = 1196 MeV
1196 MeV... Shen Qi compared the particle information list on the exam paper, so x is a Σ-particle?
Ring ring!
Just then, the bell rang for the papers to be handed in.
Shen Qi, suppressing the ringing of the bell, wrote the final answer on the exam paper: x is a Σ-particle.
It truly is a race against time, a survival version of a race against time.
Even though the exam was handed in hastily, without even a minute to check it, a top student should still walk out of the exam room calmly and gracefully. This is also a basic quality that a top student should possess.
Shen Qi walked out of the examination room with composure and elegance. Ah, a light rain was falling from the sky. What an unusual day.
"It will be very difficult to get full marks on the theory questions in this national finals. From the preliminary round to the semi-finals, and from the semi-finals to the finals, I participated in three physics competition theory exams. The worst-case scenario is that I might not get full marks on any of the theory exams." Shen Qi walked in the drizzling rain.
"Shen Qi!" Suddenly a voice called out from behind, Mu Rong caught up with an umbrella in her hand.
Mu Rong held up an umbrella, the bottom of which was just big enough to accommodate both the teacher and the student. "How did the exam go?"
"Let me hold the umbrella." Shen Qi took the umbrella. He was more than ten centimeters taller than Mu Rong had a hard time holding the umbrella.
"You seem quite calm," Mu Rong observed Shen Qi's expression.
Shen Qi murmured, "With bamboo staff and straw sandals, I travel lighter than on horseback; who's afraid?"
"Let life take its course amidst the misty rain." Mu Rong immediately followed with the next line, then cautiously inquired, "Shen, you've fully recovered and are getting full marks again?"