Chapter 12: Do the questions after entering the door
"Brother Chuan is here."
"Brother Chuan, I heard that you went to the math competition this year. How is it there? Is it fun?"
"I heard that this year's number competition is difficult. There are only twelve people who got full marks in the provincial competition, and Brother Chuan is one of them!"
"Not only that, don't forget about the provincial competition of our sports competition. Brother Chuan also scored perfect marks."
"Awesome! As expected of Brother Chuan. This is the last time. Brother Chuan definitely wants to win the double gold medal."
At Yali Middle School, with the arrival of Xu Chuan, the provincial training team quickly became lively, and all the students in the classroom came together.
As someone who has made it to the provincial team for three consecutive years, most of the students in front of him knew Xu Chuan.
After all, those who can enter the provincial team are basically students in their second and third years of high school. Students who came to experience the competition in their first year of high school also got to know this great figure under the introduction of old students.
A player who can win a gold medal in a world-class competition as a sophomore in high school is regarded as an incredibly powerful player in the eyes of all students participating in the competition.
"Hey, Xu Chuan is here."
Outside the noisy classroom, an unexpected sound came.
Xu Chuan turned around and greeted the visitor respectfully.
"Teacher Xu."
Xu Cheng looked at the student in front of him with a smile and nodded, as a greeting.
The student in front of me was taught by him last year, but I heard that he participated in the math competition this year and got full marks to enter the provincial team.
And I heard from the old guy on the math competition side that his math ability is stronger than his physics ability.
Xu Cheng scoffed at this statement.
Don't you just want to rob people? Why do you have so many tricks?
It’s not that there aren’t some who participate in both math competitions and physical competitions, but in recent years, there aren’t many in southern Hunan who can enter the provincial team and the Golden Autumn Camp and the Winter Camp at the same time. There are a few in Mingyue City and Zhongcheng.
There is no one in China who can win gold medals at both IMO and IPHO in the same year.
There are only two or three people who can be selected into the national training teams for mathematics and physics in the same year. From the time when domestic teams were formed to participate in international competitions in the 1990s to now, more than 30 years ago.
After all, the gap between digital competition and physical competition is still quite large. It is too difficult to reach the top in both aspects.
Xu Cheng is still looking forward to Xu Chuan.
He is very clear about this student's physical ability and learning ability. After one and a half years of study, he can get a gold medal at IPHO. It can be said that he can definitely win another gold medal this year.
Even the first place winner is not something we can’t look forward to.
However, expectations were expectations, and Xu Chuan was still a little dissatisfied when he went to engage in a number competition.
After all, human energy is limited. If you engage in mathematics, you will have less energy to focus on physics.
So he planned to use the questions to test it. If there was no progress, don't blame his subordinates for practicing ruthlessly to death for the next month.
Such a talented person doesn't come to study physics, but to learn mathematics from a model worker? Moreover, he is obviously a genius discovered in physics, so what does it mean to snatch someone away from him in the middle of mathematics?
Don’t even think about it!
"Come on, come on, do some questions first and let me see your learning results in the past year."
After saying hello, Xu Cheng picked up the chalk on the podium, stood in front of the blackboard and thought for half a minute, and then started to write.
"Bosons do not obey the Pauli exclusion principle and experience dramatic Bose-Einstein condensation (BEC) phenomena at low temperatures or high densities."
"This is an interesting quantum collective state achieved through phase transition."
".BEC occurs when the de Broglie wavelength corresponding to the root mean square velocity of atoms is approximately equivalent to the characteristic distance between particles in the gas.
1. For non-interacting 87Rb gas atoms in thermal equilibrium, write down the expressions of their typical momentum p and de Broglie wavelength λdB, expressed in terms of atomic mass m, temperature T and physical constants.
2. Calculate the functional relationship between the typical distance l between particles in the gas and the particle number density n. Then the expression of critical temperature Tc is derived, expressed in terms of atomic mass, density and physical constants.
3. In order to achieve BEC in the laboratory, experimenters need to lower the temperature of the gas to Tc=100nK.
If BEC occurs at this temperature, what is the number density nc of 87Rb gas? For the convenience of comparison, the number density n0 of ordinary ideal gases at standard temperature and pressure is also calculated, that is, T0=300K, p0=105Pa. It can be assumed that the mass of an atom is equal to 87 atomic mass units (mamu). What is the density n0 of ordinary gases? How many times is it nc? .
Under the podium, all the students looked confused and wondered whether they had traveled through time on the first day of training.
What is this written about? No matter how you look at it, you can’t understand it?
Only a few students frowned and stared at the question on the blackboard that almost occupied the entire blackboard.
"This question is relatively difficult. It applies some mathematical knowledge. You can use it as an extracurricular test. If you are interested, you can try to solve it. Except for Xu Chuan, please give me the answer tomorrow morning. I heard that you are taking the provincial math competition test. It shouldn’t be difficult for you if you get full marks.”
Xu Cheng threw the chalk tip in his hand towards the podium, stared at Xu Chuan and said.
The corner of Xu Chuan's mouth twitched, and he probably understood that this was Xu Cheng's dissatisfaction, dissatisfaction with him running to participate in the number competition.
But seriously, ordinary high school students may not be able to solve this question, even if they have the ability to join the national training team.
The difficulty level is almost the same as that of IPHO. Putting it on IPHO, it is almost the penultimate question type.
This question tests Bose-Einstein condensation. The whole question has three parts. The first part is not very difficult and can be solved with a certain physical foundation.
But the difficulty of the second and third parts skyrocketed, and it was like riding a rocket. Whether it was to find the root-mean-square velocity based on the average kinetic energy of the atom, or to find the de Broglie wavelength after finding the momentum, the difficulty was not ordinary. High school students can handle it.
The difficulty of finding the distance between particles in the third step is even higher.
If the first question is 1+2=3, then the second and third questions are so difficult that they have to prove 1+2=3.
Compared with the math competition questions, the calculation amount of this question is actually not large, but it requires the solver's logical ability and application ability to be very high.
But this is the ability required to study physics.
After all, the difference between physics and mathematics is quite big.
In the process of systematic learning, the difficulty of mathematics lies in the cultivation of thinking, while the difficulty of physics lies in the application of knowledge and methods.
(End of chapter)