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Gemiola [76]
3 years ago
14

Suppose a two-level system is in a bath with temperature 247 K. The energy difference between the two states is 1.1 × 10-21 J. W

hat is the probability that we will find the system in the higher energy state?
Physics
1 answer:
Alik [6]3 years ago
4 0

Answer:

The probability of higher energy state is 0.4200.

Explanation:

Given that,

Temperature = 247 K

Energy difference between two states E_{2}-E_{1}=1.1\times10^{-21}\ J

We need to calculate the probability of higher energy state

Probability of E_{1}= e^{-\beta E_{1}}

Probability of E_{2}= e^{-\beta E_{2}}

The total probability is

e^{-\beta E_{1}}+e^{-\beta E_{1}}=1

Here, E₁ = lower energy state

E₂ = higher energy state

Put the value of E₁ in to the formula

e^{-\beta(E_{2}-1.1\times10^{-21})}+e^{-\beta E_{1}}=1

e^{-\beta E_{2}}(e^{\beta 1.1\times10^{-21}}+1)=1

e^{\beta E_{2}}=\dfrac{1}{1+e^{\dfrac{1.1\times10^{-21}}{KT}}}

Here, \beta=\dfrac{1}{KT}

Put the value into the formula

e^{\beta E_{2}}=\dfrac{1}{1+e^{\dfrac{1.1\times10^{-21}}{1.380\times10^{-23}\times247}}}

e^{\beta E_{2}}=0.4200

Hence, The probability of higher energy state is 0.4200.

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