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Energy of a photon of wavelength 5890Åemitted by sodium vapour lamp is
Question

Energy of a photon of wavelength 5890Åemitted by sodium vapour lamp is

A.

2.1 J

B.

2.1 MeV

C.

2.1 eV

D.

2.1 Cal

Correct option is C

Given:Wavelength, λ=5890 A˚=5890×1010 mSpeed of light, c=3×108 m/sPlanck’s constant, h=6.626×1034 Js1 eV=1.602×1019 JFormula E=hcλE=6.626×1034×3×1085890×1010E3.3748×1019 JNow convert joules to eV:E=3.3748×10191.602×10192.1 eV\textbf{Given:} \\\bullet \text{Wavelength, } \lambda = 5890\, \text{\AA} = 5890 \times 10^{-10}\, \text{m} \\\bullet \text{Speed of light, } c = 3 \times 10^8\, \text{m/s} \\\bullet \text{Planck's constant, } h = 6.626 \times 10^{-34}\, \text{J} \cdot \text{s} \\\bullet 1\, \text{eV} = 1.602 \times 10^{-19}\, \text{J}\\[10pt]\textbf{Formula } \\E = \frac{hc}{\lambda}\\[10pt]E = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{5890 \times 10^{-10}} \\E \approx 3.3748 \times 10^{-19}\, \text{J}\\[10pt]\text{Now convert joules to eV:} \\E = \frac{3.3748 \times 10^{-19}}{1.602 \times 10^{-19}} \approx 2.1\, \text{eV}​​

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