A cube of unit volume contains 35 times 10^7 | vedclass

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Question

(A) The total energy $E$ of the photons in the unit volume is given by $E = N 	imes hf$,where $N = 35 	imes 10^7$,$h = 6 	imes 10^{-34} 	ext{ Js}$

Vedclass · Accepted Answer

$22.98$

Vedclass · Answer

(A) The total energy $E$ of the photons in the unit volume is given by $E = N 	imes hf$,where $N = 35 	imes 10^7$,$h = 6 	imes 10^{-34} 	ext{ Js}$,and $f = 10^{15} 	ext{ Hz}$.$E = (35 	imes 10^7) 	imes (6 	imes 10^{-34}) 	imes 10^{15} = 210 	imes 10^{-12} = 2.1 	imes 10^{-10} 	ext{ J}$.The energy density $u$ of an electromagnetic wave is given by $u = \frac{B_0^2}{2\mu_0}$,where $B_0$ is the amplitude of the magnetic field.Since the volume $V = 1 	ext{ m}^3$,the total energy $E = u 	imes V = \frac{B_0^2}{2\mu_0} 	imes 1$.Equating the energies: $2.1 	imes 10^{-10} = \frac{B_0^2}{2 	imes 4\pi 	imes 10^{-7}}$.$B_0^2 = 2.1 	imes 10^{-10} 	imes 8\pi 	imes 10^{-7} = 16.8\pi 	imes 10^{-17}$.Using $\pi = \frac{22}{7}$,$B_0^2 = 16.8 	imes \frac{22}{7} 	imes 10^{-17} = 2.4 	imes 22 	imes 10^{-17} = 52.8 	imes 10^{-17} = 528 	imes 10^{-18}$.$B_0 = \sqrt{528} 	imes 10^{-9} \approx 22.978 	imes 10^{-9} 	ext{ T}$.Thus,$\alpha \approx 22.98$.

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