A 4.4 × $10^{14}$ Hz laser emits a 2.1 μs pulse that is 5.0 mm in diameter.The energy density in the beam is $0.24 \mathrm {~J} / \mathrm { m } ^ { 3 }$ How many wavelengths are there in the length of the beam? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T ∙ m/A,ε₀ = 8.85 × 10^-12 C²/N ∙ m²) A)9.2 × 10⁸ B)2.8 × 10⁹ C)2.8 × 10⁸ D)9.2 × 10⁹ E)2.8 × 10¹⁰

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Quizplus · Accepted Answer

The wavelength is given by:$$\lambda = \frac{c}{f} = \frac{3.0 	imes 10^8 	ext{ m/s}}{4.4 	imes 10^{14} 	ext{ Hz}} = 6.82 	imes 10^{-7} 	ext{ m}$$The length of the beam is:$$L = ct = (3.0 	imes 10^8 	ext{ m/s})(2.1 	imes 10^{-6} 	ext{ s}) = 0.63 	ext{ m}$$The number of wavelengths in the length of the beam is:$$N = \frac{L}{\lambda} = \frac{0.63 	ext{ m}}{6.82 	imes 10^{-7} 	ext{ m}} = 9.2 	imes 10^8$$

A 44 × 101410^{14}1014 Hz Laser Emits a 2 0.24 J/m30.24 \mathrm {~J} / \mathrm { m } ^ { 3 }0.24 J/m3

A 44 × $10^{14}$ Hz Laser Emits a 2 $0.24 \mathrm {~J} / \mathrm { m } ^ { 3 }$