Question

Q.1 and 2
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Answer 1

Answer on Question #42888, Physics, Molecular Physics | Thermodynamics

Task:

1. A paramagnetic gas at temperature $27{}^{\circ}\mathrm{C}$ is placed in an external uniform H magnetic field of magnitude 1.5 T. If the atoms of the gas have magnetic dipole moment $\mu = 2.0\mu_{B}$, then the energy difference between parallel alignment and antiparallel alignment of the atom's magnetic dipole moment with the magnetic field is:

(a) $2.3 \times 10^{-22} \, \mathrm{J}$

(b) $5.6 \times 10^{-23} \, \mathrm{J}$

(c) $1.9 \times 10^{-24} \, \mathrm{J}$

(d) $1.6 \times 10^{-25} \, \mathrm{J}$

Solution:

$$\theta_{1} = 0, \theta_{2} = 180{}^{\circ}, \mu_{B} = 9.27 \cdot 10^{-24} \, \mathrm{J} / \mathrm{T}.$$ $$\mu H (\cos \theta_{1} - \cos \theta_{2}) = 2 \mu H = 4 \mu_{B} \cdot 1.5 = 6 \cdot 9.27 \cdot 10^{-24} \approx 5.6 \cdot 10^{-23} \, \mathrm{J}.$$

Answer: (b) $5.6 \times 10^{-23} \, \mathrm{J}$

2. A series RLC circuit has inductance $L = 12 \, \mathrm{mH}$, capacitance $C = 1.2 \, \mu \mathrm{F}$, and resistance $R = 12 \, \Omega$. At what time will the amplitude of the charge oscillations in the circuit be $10\%$ of its initial value?

(a) 2.0 ms

(b) 3.0 ms

(c) 4.0 ms

(d) 5.0 ms

Solution:

$$\ln \frac{A_{0} e^{-\beta t}}{A_{0} e^{-\beta (t + \Delta t)}} = \ln (1 / 0.1) = \beta \Delta t = \frac{2R}{L} \Delta t \Rightarrow \Delta t = \frac{\ln (1 / 0.1) L}{2R} \approx 2.0 \, \mathrm{ms}$$

Answer: (a) 2.0 ms

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