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Numerical · Q34

Q.Calculate the wavelength in nm of an X-ray wave of frequency 2.0×\times1018^{18} Hz.

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Rearranging c=νλc=\nu\lambda for wavelength gives λ=cν=3.0×108 m/s2.0×1018 Hz=1.5×10−10\lambda=\dfrac{c}{\nu}=\dfrac{3.0\times10^{8}\ \text{m/s}}{2.0\times10^{18}\ \text{Hz}}=1.5\times10^{-10} m. Converting to nanometres (1 nm =10−9=10^{-9} m) gives λ=1.5×10−10 m=0.15×10−9 m=0.15\lambda=1.5\times10^{-10}\ \text{m}=0.15\times10^{-9}\ \text{m}=0.15 nm -- a value that also sits comfortably within the X-ray wavelength range quoted in Table 13.1 (1×10−111\times10^{-11} to 3×10−83\times10^{-8} m), confirming the answer is physically consistent with the wave being described as an X-ray. [!ANSWER] λ\lambda = 0.15 nm

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