Question

A photon of wavelength \(500\,nm\) is incident on a metal surface. The energy of the photon is approximately \((h=6.63\times10^{-34}\,Js,\; c=3\times10^8\,m/s)\)

• A. \(1.99\times10^{-19}\,J\)
• B. \(3.98\times10^{-19}\,J\)
• C. \(5.97\times10^{-19}\,J\)
• D. \(7.96\times10^{-19}\,J\)

Hint:

Photon Energy: \[ \boxed{E=\frac{hc}{\lambda}} \] Useful shortcut: \[ \boxed{E(eV)=\frac{1240}{\lambda(nm)}} \] For shorter wavelength: \[ \boxed{\text{Higher Energy}} \]

Answer 1

The Correct Option is B

Step 1: Recall the photon energy relation. \[ E=\frac{hc}{\lambda} \] Given: \[ h=6.63\times10^{-34}\,Js \] \[ c=3\times10^8\,m/s \] \[ \lambda=500\times10^{-9}\,m \]

Step 2: Substitute the values. \[ E= \frac{(6.63\times10^{-34})(3\times10^8)} {500\times10^{-9}} \] \[ E= \frac{19.89\times10^{-26}} {5\times10^{-7}} \] \[ E=3.98\times10^{-19}\,J \]

Step 3: Choose the correct option. \[ \boxed{E=3.98\times10^{-19}\,J} \] Therefore, \[ \boxed{\text{(B)}} \] is the correct answer.