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18 lines
1.6 KiB
Plaintext
18 lines
1.6 KiB
Plaintext
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Please provide a clear and step-by-step solution for a scientific problem in the categories of Chemistry, Physics, or Mathematics. The problem will specify the unit of measurement, which should not be included in the answer. Express the final answer as a decimal number with three digits after the decimal point. Conclude the answer by stating 'Therefore, the answer is \boxed[ANSWER].
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Promblem 1: A one-particle, one-dimensional system has $\Psi=a^{-1 / 2} e^{-|x| / a}$ at $t=0$, where $a=1.0000 \mathrm{~nm}$. At $t=0$, the particle's position is measured. (b) Find the probability that the measured value is between $x=0$ and $x=2 \mathrm{~nm}$.
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Answer: The answer is \boxed{0.4908}.
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Promblem 2: Calculate the ground-state energy of the hydrogen atom using SI units and convert the result to electronvolts.
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Answer: The answer is \boxed{-13.598 }.
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Promblem 3: The strongest infrared band of ${ }^{12} \mathrm{C}^{16} \mathrm{O}$ occurs at $\widetilde{\nu}=2143 \mathrm{~cm}^{-1}$. Find the force constant of ${ }^{12} \mathrm{C}^{16} \mathrm{O}$.
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Answer: The answer is \boxed{1855}.
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Promblem 4: Find the probability that the electron in the ground-state $\mathrm{H}$ atom is less than a distance $a$ from the nucleus.
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Answer: The answer is \boxed{0.323}.
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Promblem 5: A one-particle, one-dimensional system has $\Psi=a^{-1 / 2} e^{-|x| / a}$ at $t=0$, where $a=1.0000 \mathrm{~nm}$. At $t=0$, the particle's position is measured. (a) Find the probability that the measured value lies between $x=1.5000 \mathrm{~nm}$ and $x=1.5001 \mathrm{~nm}$.
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Answer: The answer is \boxed{4.979}.
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