The three days of the Mathematical Modeling Contest will just wash away two big lessons.

Although it was ordered to ask for leave, considering that it was not good to ask for leave in the first class, Lu Zhou decided to send the leave slip in person, so as not to trouble the squad leader.

Looking at the timetable information given by the Academic Affairs Office, the name of the teacher is Li Rongen, and he is an old professor with high qualifications. After asking for the phone number in the school group, Lu Zhou first called to confirm that the teacher was in the office, and then went over with a fake note.

After knocking on the door, Lu Zhou walked in, put the fake note on the desk, and explained his intention.

"Leave?" After glancing at the fake note, Professor Li took off his reading glasses, raised his head and smiled, "Your name is Lu Zhou, right?" ”

"Yes." Lu Zhou nodded.

Professor Li smiled and said, "Okay, I'll test you two questions, and if you solve one, I'll approve your fake note." ”

And this kind of operation?!

Lu Zhou was dumbfounded.

"What? Scared? Li Rongen asked with a smile.

"No," Lu Zhou froze, shook his head, and said, "Teacher, you can solve the question." ”

"The first question, take it," throwing an A4 piece of paper into Lu Zhou's hand, Li Rongen looked at Lu Zhou with a smile, and the old god said on the ground, "I want to see the process as much as I can write." ”

Even the question is ready?!

Lu Zhou always felt that this guy was premeditated, otherwise how to explain why this question had been printed on A4 paper?

However, even if he guessed a little, Lu Zhou didn't say anything, picked up the A4 paper and began to read the question.

[The half-life of the U238 nucleus in the nuclear submarine is 4.5×10^9 years, and there is a 0.7% probability of becoming the U234 nucleus in the decay, and at the same time a high-energy photon is released, 93% of which are absorbed by the submarine steel plate. In 1981, the high-energy photons transmitted to the outer part of the Soviet nuclear submarine U137 were measured by a detector at a distance of 1.5 m from the nuclear source (processed as a point). The instrument has a positive incident area of 22cm^2 and an efficiency of 0.25% (one pulse signal can be generated for every 400 incident photons), and 125 signals are measured per hour.

(1) Find the average lifetime of U238 nuclei (ln2=0.693).

(2) Find the mass of U238 in the nuclear submarine (unit kg, take 2 digits)

】

After reading the title, Lu Zhou sighed softly in his heart.

is worthy of Professor Li, who was named the "Four Demons of the Academy of Things" by his predecessors in the past, is this kind of topic when he makes a move?

In other words, the first big things class will be held next Monday, and it is really no problem to directly test yourself with this kind of nuclear physics knowledge that plays beyond the curriculum?

"Why don't you find a place to sit?"

"No, here it is."

Taking the pen and scratch paper that Professor Li handed him casually, Lu Zhou stood next to his desk, frowned, and thought for a moment.

Physics is really not his area of expertise.

However, after a summer of liver-bursting study, he is impeccable standing here!

About five minutes passed, Lu Zhou's brows relaxed, and the tip of his pen moved.

[Decay law of radionuclides: N=N0e^(-λt)

The relationship between the decay constant and the half-life is: N0/2=N0e^(-λT1/2), from which T1/2=ln2/λ is obtained

】

Writing down these two lines of calculations, Lu Zhou's eyes flickered slightly.

He has succeeded in turning a physics problem into a high-math problem.

Next, it's a matter of breaking them one by one!

First of all, the first question!

The nib of the pen moves quickly across the A4 paper.

[(1) The average lifetime of radionuclides t = ∫λNtdt/N0 = ...... = 1.1443T1/2

Substituting data can be obtained, t=6.49*10^9 years.

】

Glancing at the A4 paper, Professor Li Rongen raised his eyebrows, and an interesting look appeared in his eyes.

Not noticing the change in Professor Li's expression, his attention was highly focused on Lu Zhou on the paper, and he began to continue to answer the next question.

[From the stem information, it can be solved that the number of high-energy photons produced by decaying into U234 at dt time is -dN·n0=n0λNdt.]

Then let the efficiency of photons passing through the steel plate be n1, and calculate the number of photons passing through the steel plate in dt time as dN1=n0λNdt·n1

Number of photons entering the detector......

Number of signals produced in the detector......

The number of U238 in the submarine is calculated, and the number of U238 nuclei is calculated from this.

】

Lu Zhou substituted all the data and calculated the number of U238 nuclei in the submarine N=7.456*10^25.

However, just as he was about to bring N into M=N*238u and complete the final blow to the enemy's spring, Professor Li Rongen suddenly spoke.

"Okay, you've got it."

Lu Zhou: ???

He was immediately unhappy.

What does it mean to count me over?

I've got it all here, can't you wait for me to finish talking!

"Professor, I'm not done with ...... yet"

"You've calculated it to this point, and you can figure it out if you find a junior high school student," Li Rongen said with a smile, "If you want to do it, it's up to you." ”

The atmosphere of doing the questions was destroyed, and Lu Zhou was speechless for a while.

couldn't stand the entanglement of obsessive-compulsive disorder, and he still wrote the results at the end.

The answer M = 29.634kg, take two digits and take about 30kg

The steps are correct, and the results are undoubtedly correct.

Lu Zhou brought this question to a successful conclusion.

"Would you like to hear the second question?" Li Rongen said with a smile.

Although Lu Zhou wanted to say "I don't want to", he couldn't help but say helplessly when he thought that the professor hadn't approved his fake note: "Say it." ”

Li Rongen smiled and continued: "Don't be nervous, the second question is very simple, you can tell me about the Kennan formulation of the second law of thermodynamics." ”

Hearing this question, Lu Zhou breathed a sigh of relief.

Originally, he thought that this professor's second question would debut a difficult problem that he couldn't write at all, knocking him and warning him not to be complacent or something, but he didn't expect that Professor Li didn't play cards according to the routine at all, so he simply let him go.

Generally speaking, there are two main formulations of the second law of thermodynamics, one is the famous Kelvin formulation and the other is the formulation mentioned by Clausius in his 1850 paper.

As for Kennan's formulation, it is a relatively new formulation that has been produced recently.

If you read the textbook carefully, you won't miss it.

i.e. –

"For a system with a given energy, composition of matter, and parameters, there is a stable equilibrium state in which other states can always be achieved by reversible processes." As if by memorizing a text, Lu Zhou repeated this statement.

"Not bad." Li Rongen nodded approvingly.

In the textbooks used by non-physics majors, this more cutting-edge expression will not be mentioned in the main text, but it will still be mentioned in the appendix. Generally, students who are not interested in physics will not go there after graduation.

If Lu Zhou even grasped this cold knowledge point so clearly, it was enough to prove that he had thoroughly eaten the entire "College Physics" textbook.

After this shallow and in-depth investigation, Li Rongen can now confirm that his course for undergraduate non-physics students really has nothing to teach him.

It seems that Lao Tang really didn't brag, this kid is a talent!

In fact, what is said to be a fake after answering the question correctly, it is all a joke with young people.

Since yesterday, he has approved dozens of fake notes for the mathematical modeling competition, will there be such a fake note?

Even if Lu Zhou can't answer, he will ridicule at most two sentences, and he will still approve it in the end.

After signing the fake note, Li Rongen took out the roll call book in the drawer, and said in the voice of an elder while drawing two checks on it.

"Lu Zhou."

"What's wrong?"

"Do you have any plans to go to graduate school?"

Lu Zhou thought for a while and said in an uncertain tone, "Yes." ”

Who can say what the future holds?

However, Professor Li's intuition was obviously not as keen as that of Old Tang, and he didn't hear the uncertainty in Lu Zhou's tone at all, but nodded approvingly, and then continued.

"The Department of Physics of our NTU is also considered to be the top level among universities in the country, and modestly speaking, even if Peking University and us are tied for the first place. However, when it comes to specific research directions, they are inferior to us in the fields of superconducting physics and strongly correlated electronic systems, as well as condensed matter physics and materials design. If you are interested in physics, you can come to me when you are admitted to graduate school, our carbon nanotube laboratory needs top talents in the field of mathematics. ”

This is......

Is it implying to me that I will later enroll in his graduate school?

Lu Zhou couldn't cry or laugh in his heart, he was just a sophomore now, and he was still far from the graduate school entrance examination.

But no matter what you say, it's all the kindness of the teacher.

Lu Zhou said sincerely: "Thank you, teacher." ”

Li Rongen smiled and nodded: "Okay, let's take the fake note." This kind of competition has the opportunity to participate in more if you are a politician. If you can't cure it, you can pay attention to the opportunity of the next research institute. Or when you reach your junior year next year, come and ask me, ask you Mr. Tang, it's okay. ”

Lu Zhou smiled and expressed his gratitude, didn't say anything more, and quickly took this hard-won fake note and said goodbye.