Translator: Henyee Translations Editor: Henyee Translations
There were two physics lessons during the three days of the mathematical modeling competition.
Lu Zhou felt like it was not a good impression to miss the first class and so, he decided to personally hand in the permission slip as he did not want to bother the class leader.
From the class information given by the Academic Affairs Office, the physics teacher was called Li Rongen and he was an old professor with high qualifications. When Lu Zhou found his phone number, he gave him a call to confirm that he was in his office before he headed over.
Lu Zhou knocked on the door before he walked in. He handed the permission slip on the desk and explained his reasons.
“Permission to miss classes?” said Professor Li. He took off his glasses and looked at the slip as he said, “Your name is Lu Zhou, right?”
“Yes,” said Lu Zhou as he nodded.
Professor Li smiled and said, “Okay, then let me ask you two questions. If you can answer one of them, I’ll approve your permission slip.”
What’s this?
Lu Zhou was stunned.
“What? Scared?” asked Li Rongen with a smile.
“Nope,” said Lu Zhou. He fixed his composure, shook his head, and said, “Professor, please go ahead and ask me.”
“The first question, take this,” said Li Rongen as he handed Lu Zhou an A4 sized paper. With a smile, he said, “Write as much as you want. I want to see the working.”
You even prepared the questions?
Lu Zhou felt like the man premeditated this. Otherwise, why would the question be printed on an A4 paper?
Lu Zhou did not say anything as he took the A4 paper and started to read the question.
[The half-life of uranium 238 in a nuclear submarine is 4.5×10^9 years. There is a 0.7% probability of a uranium 234 decay, which will release a high-energy photon, 93% of which is absorbed by the submarine steel plates. In 1981, a nuclear submarine from the Soviet Union transmitted a high-energy photo, which was measured by the detector 1.5m from the nuclear source (treat the source as a point). The instrument’s positive incident area is 22cm^2, the efficiency is 0.25% (one pulse signal per 400 incident photos), 125 signals are measured per hour.
1. Find the average life of the uranium 238 core. (ln2 = 0.693)
2. Find the mass of uranium 238 in the submarine (kg as a unit, 2 sig figs)
]
Lu Zhou finished reading the question and sighed in his heart.
No wonder he is named one of the “four physics devil” professors. What a question!
Speaking of which, the first physics lecture is next Monday. Why is she asking me this nuclear physics question?
“Do you want to sit down?”
“It’s okay, I’ll stand.”
Lu Zhou took the pen and draft paper from Professor Li. He stood next to the office table. With a frown, he began to think.
Physics was not his strong suit.
However, after an entire summer of grinding, he was invulnerable!
Five minutes passed and Lu Zhou relaxed before he started to write.
[Law of decay: N=N0e^(-λt)
The relationship between the decay constant and half-life constant is: N0/2=N0e^(-λT1/2), from which T1/2=ln2/λ
]
Lu Zhou wrote down the two equations and his eyes flashed.
He had successfully turned a physics problem into an advanced algebra problem.
Next up, he just had to solve it!
First part!
The pen moved quickly on the A4 paper.
[(1) Average lifetime of radionuclide t=∫λNtdt/N0=…=1.1443T1/2
Substituting data gives T=6.49*10^9 years.
]
Professor Li looked at that A4 paper with his eyebrows raised and he had a look of interest in his eyes.
Lu Zhou did not notice Professor Li’s change of expression. He was too concentrated on the question as he began to answer the next part.
[From the information provided, the number of high-energy photons generated by decaying to U234 at dt time is dN·n0=n0λNdt]
Let the efficiency of photons passing through the steel plate as n1, and the number of photons passing through the steel plate in the dt time is calculated as dN1=n0λNdt·n1
The number of photons entering the detector…
The number of signals generated…
Able to calculate the number of uranium 238 in the submarine, which gives the mass.
]
Lu Zhou substituted all of the data and calculated the number of uranium 238 as N = 7.456×10^25.
However, just he was preparing to substitute N to calculate the mass and complete the final blow to the enemy, Professor Li suddenly spoke.
“Okay, I’ll count that you passed.”
Lu Zhou: ? ? ?
He was not happy at all.
What do you mean you’ll count that I passed?
I already did it up to this point. Can’t you just let me finish before speaking!
“Professor, I haven’t finished…”
“A middle school student can finish this step,” said Li Rongen. With a smile, he said, “You can finish it if you want.”
The momentum of solving the question was destroyed and Lu Zhou was left speechless.
His OCD forced him to finish the question.
Answer M = 29.634kg, two sig fig as 30kg.
The steps were right and the answer was definitely correct.
Lu Zhou wrote down a full stop as he completed the question.
“Do you want to hear the second question?” asked Li Rongen with a smile.
Although Lu Zhou wanted to say “No”, he remembered that the professor had not signed the permission slip yet, so he replied, “Say it.”
Li Rongen laughed and said, “Don’t be nervous, the second question is very easy. Just tell me the second law of thermodynamics.”
When Lu Zhou heard this question, he sighed in relief.
He thought that the professor would give him an impossible question to defeat him and to destroy his ego. He had not expected to be set free by Professor Li.
Normally speaking, there were two different expressions of the second law of thermodynamics. One was the famous Kelvin equation, the other was the expression mentioned by Rudolf Clausius in the 1850 thesis.
As for Hatsopoulos-Keenan’s expression, it was a relatively new expression that only recently emerged.
Lu Zhou read the textbook carefully and so he did not miss it.
“For a system with a given energy, material composition, and parameters, there is a stable equilibrium state. Other states can always be achieved through a reversible process,” said Lu Zhou as he recited this expression effortlessly.
“Not bad,” said Li Rongen as he nodded with approval.
The textbooks used by physics majors did not mention the more advanced expression in the text even though they might have mentioned it in the appendix. Students who were not interested in physics would never know this expression.
Lu Zhou even recited this obscure fact, which proves that he had thoroughly understood the [University Physics] textbook.
After this investigation, Li Rongen could confirm that there was not anything an undergraduate physics course could teach Lu Zhou.
I guess Old Tang wasn’t bragging, this kid is talented!
He would have signed the permission slip regardless as he was only joking around.
Since yesterday, he had signed dozens of permission slips for the mathematical model. Another one would not be any problem.
Even if Lu Zhou did not answer, he would have just roasted Lu Zhou a bit but he would still sign it.
Li Rongen signed his signature before pulling out a name list from his drawer. He drew two ticks on it before he spoke with an elderly tone.
“Lu Zhou.”
“What?”
“Do you have plans for a master’s?
Lu Zhou thought and said with an uncertain tone, “Sure.”
Who knows what can happen in the future?
However, Professor Li’s intuition was weaker than Professor Tang’s. He did not hear the uncertainty in Lu Zhou’s tone. Instead, he merely nodded his head in approval and continued.
“The physics department of our University of Jin Ling is one of the best in the nation. Humbly speaking, we’re tied for first. But for superconducting physics, electronic system, condensed physics, and material design, they are not as good as us. We are the best. IF you are interested in physics, come to our carbon nanotubes laboratory when you graduate. We are always looking for talented mathematicians.”
This is…
Is he implying that I should apply to be his graduate student?
Lu Zhou laughed. He was only a second year and was still far from doing a master’s.
Regardless, the teacher was being kind.
Lu Zhou sincerely said, “Thank you, professor.”
Li Rongen smiled and nodded his head, “Okay, take the permission slip and leave. You should enter more competitions like this if you can. If you want to do a master’s, you should watch out for a guaranteed master’s spot. Or you can wait till you’re in the third year and ask me or Professor Tang, whatever you want.”
Lu Zhou smiled and expressed his gratitude. Without saying anything else, he took his hard-earned permission slip and left.