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NEET CHEMISTRYEasy

A particular station of All India Radio, New Delhi, broadcasts on a frequency of 1,368 kHz1,368 \text{ kHz} (kilohertz). The wavelength of the electromagnetic radiation emitted by the transmitter is: [speed of light, c=3.0×108 m s1c = 3.0 \times 10^8 \text{ m s}^{-1}]

A

2192 m

B

21.92 cm

C

219.3 m

D

219.2 m

Step-by-Step Solution

The wavelength (λ\lambda), frequency (ν\nu), and speed of light (cc) are related by the equation: c=νλλ=cνc = \nu \lambda \Rightarrow \lambda = \frac{c}{\nu}

  1. Identify Given Values: Frequency (ν\nu) = 1368 kHz=1368×103 s11368 \text{ kHz} = 1368 \times 10^3 \text{ s}^{-1} (or Hz) Speed of light (cc) = 3.0×108 m s13.0 \times 10^8 \text{ m s}^{-1}

  2. Calculate Wavelength (λ\lambda): λ=3.0×108 m s11368×103 s1\lambda = \frac{3.0 \times 10^8 \text{ m s}^{-1}}{1368 \times 10^3 \text{ s}^{-1}} λ=3000×10513.68×105 m\lambda = \frac{3000 \times 10^5}{13.68 \times 10^5} \text{ m} (Adjusting powers for easier division) λ=3.0×1081.368×106 m\lambda = \frac{3.0 \times 10^8}{1.368 \times 10^6} \text{ m} λ=219.298... m\lambda = 219.298... \text{ m}

  3. Rounding: Rounding to one decimal place, λ219.3 m\lambda \approx 219.3 \text{ m}.

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