Question

A two-state system is in an environment at temperature 500 K. The energy of state 1 is 4.1e-20 J, and the energy of state 2 is 5.7e-20 J. Let be the probability of finding the system in state 1, and be the probability of finding the system in state 2. What is the ratio

Answer 1

Complete Question

A two-state system is in an environment at temperature 500 K. The energy of state 1 is$E_1=4.1e-20 J$, and the energy of state 2 is $E_2= 5.7e-20 J$. Let P(1) be the probability of finding the system in state 1, and be the probability of finding the system in state 2. What is the ratio P(2)/P(1)

Answer:

 $X=0.0984$

Step-by-step explanation:

From the question we are told that:

Temperature T=500 K

Energy of state 1 $E_1=4.1e-20 J$,

Energy of state 2 is $E_2= 5.7e-20 J$

Generally the equation for Probability of finding the system in state is mathematically given by

 $P(1)=e ^{\frac{-E_1}{KT}}$

Therefore

For Probability of finding the system in state 1 $P(1)$

 $P(1)=e ^{\frac{-E_1}{KT}}$

Where

   K is Boltzmann constant

   $K=1.38*10^{-23}$

 $P(1)=e ^{\frac{-(4.1e-20 J)}{1.38*10^{-23}*500}}$

For Probability of finding the system in state 1 $P(2)$

 $P(2)=e ^{\frac{-(5.7e-20 J)}{1.38*10^{-23}*500}}$

Generally the equation for The Ratio of $P(2)$ and $P(2)$ is mathematically given by

 $X=\frac{P(2)}{p(1)}$

 $X=e ^{\frac{E_1-E_2}{KT}}$

 $X=e ^{\frac{-(4.1-5.7)e-20 J)}{1.38*10^{-23}*500}}$

 $X=0.0984$