Question

Calculate the energy of photons having wavelength \(5\times 10^{-7}\) m falling on a metal surface of work function \(3.4\times 10^{-19}\) J.

• A. \(3.97\times 10^{-19}\) J
• B. \(3.55\times 10^{-19}\) J
• C. \(2.97\times 10^{-19}\) J
• D. \(2.57\times 10^{-19}\) J

Hint:

Always remember to use the correct values for constants: \(h = 6.626\times 10^{-34}\) Js, \(c = 3\times 10^8\) m/s.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The energy of a photon is given by the equation \(E = \frac{hc}{\lambda}\), where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.

Step 2: Detailed Explanation:
Given: \(\lambda = 5\times 10^{-7}\) m, \(h = 6.626\times 10^{-34}\) Js, \(c = 3\times 10^8\) m/s. \[ E = \frac{hc}{\lambda} = \frac{(6.626\times 10^{-34} \text{ Js}) \times (3\times 10^8 \text{ m/s})}{5\times 10^{-7} \text{ m}} \] \[ E = \frac{1.9878\times 10^{-25}}{5\times 10^{-7}} = 3.9756\times 10^{-19} \text{ J} \]

Step 3: Final Answer:
The energy of the photons is approximately \(3.97\times 10^{-19}\) J, which corresponds to option (A).