Calculate the energy in Joule corresponding to light of wavelength 45 nm: (Planck's constant h = 6.63 × 10⁻³⁴

Question

Calculate the energy in Joule corresponding to light of wavelength 45 nm: (Planck's constant h = 6.63 × 10⁻³⁴ Js; speed of light c = 3 × 10⁸ ms⁻¹)

Accepted Answer

The energy ($E$) of a photon is related to its wavelength ($\lambda$) by the Planck's equation: $E = \frac{hc}{\lambda}$.

1.  **Identify Given Values:**
    *   Planck's constant ($h$) = $6.63 	imes 10^{-34} 	ext{ Js}$
    *   Speed of light ($c$) = $3 	imes 10^8 	ext{ ms}^{-1}$
    *   Wavelength ($\lambda$) = $45 	ext{ nm} = 45 	imes 10^{-9} 	ext{ m}$

2.  **Calculation:**
    $$E = \frac{(6.63 	imes 10^{-34}) 	imes (3 	imes 10^8)}{45 	imes 10^{-9}}$$
    $$E = \frac{19.89 	imes 10^{-26}}{45 	imes 10^{-9}}$$
    $$E = 0.442 	imes 10^{-17} 	ext{ J}$$
    $$E = 4.42 	imes 10^{-18} 	ext{ J}$$

Thus, the energy corresponds to Option D.

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