Question

Calculate the energy of photon in electromagnetic radiation having wavelength \(400 \mathrm{~nm}\left(\mathrm{~h}=6.626 \times 10^{-34} \mathrm{Js} ; \mathrm{c}=3 \times 10^8 \mathrm{~ms}^{-1}\right)\).

• A. \(4.061\times 10^{-19}\text{ }\mathrm{J}\)
• B. \(4.969\times 10^{-19}\text{ }\mathrm{J}\)
• C. \(5.226\times 10^{-19}\text{ }\mathrm{J}\)
• D. \(4.118\times 10^{-19}\text{ }\mathrm{J}\)

Hint:

Use \(E=\dfrac{hc}{\lambda}\) with the wavelength in metres.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The energy of a photon is \(E=h\nu=\dfrac{hc}{\lambda}\).

Step 2: Convert units
\(\lambda=400\ \mathrm{nm}=4\times10^{-7}\ \mathrm{m}\).

Step 3: Substitute
\(E=\dfrac{6.626\times10^{-34}\times3\times10^{8}}{4\times10^{-7}}\).

Step 4: Evaluate
\(E=\dfrac{1.9878\times10^{-25}}{4\times10^{-7}}=4.969\times10^{-19}\ \mathrm{J}\).

Final Answer:
The photon energy is \(4.969\times10^{-19}\) J. \[ \boxed{\text{(B) }4.969\times 10^{-19}\text{ J}} \]