Question

Assignment 1 Exercise 21.54 7 of 8> What is the change in electric potential energy when the dipole moment of a molecule changes its orientation with respect to E from parallel to perpendicular? Express your answer using two significant figures he ammonia molecule (N 5.0 x 10-0Amonia molecules in the gas phase are placed in a uniform electric field Ewith magnitude 2.0x10 N/C Hs) has a dipole moment of Δυ-9.0.10 24 Submit Incorrect: Try Again; 5 attempts remaining Part B At what absolute temperature T is the average translational kinetic energyof a molecule equal to the change in potential energy calculated in part (a)? (Note: Above this temperature, thermal agitation prevents the dipoles from aligning with the electric field.) Express your answer using two significant figures Submit Request Answer

Answer 1

Potential Energy of a dipole in Electric field is given by:

U = -p*E*cos $\theta$

when parallel, $\theta$ = 0 & cos 0 = 1

when perpendicular, $\theta$ = 90 & cos 90 = 0

So change in potential energy will be:

dU = U(90) - U(0)

dU = -p*E*cos 90 - (-p*E*cos 0)

dU = 0 - (-p*E) = p*E

Now given that

p = 5*10^-30 C.m

E = 2*10^6 N/C

So,

dU = p*E = (5*10^-30)*(2*10^6)

dU = 1.0*10^-23 J

Part B

Now we need temperature when

3kT/2 = dU

T = 2*dU/(3k)

k = boltzmann's constant = 1.381*10^-23

So,

T = 2*1*10^-23/(3*1.381*10^-23)

T = 0.48 K

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