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

To calculate the energy of photons with a given wavelength, we can use the formula:

\(E = \frac{hc}{\lambda}\)

where:

• \(E\) is the energy of the photon
• \(h = 6.626 \times 10^{-34} \, \text{Js}\) is Planck's constant
• \(c = 3 \times 10^8 \, \text{m/s}\) is the speed of light
• \(\lambda = 5 \times 10^{-7} \, \text{m}\) is the wavelength of the photon

Substituting these values into the formula, we get:

\(E = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{5 \times 10^{-7}}\)

Calculating the above expression:

\(E = \frac{19.878 \times 10^{-26}}{5 \times 10^{-7}} = 3.9756 \times 10^{-19} \, \text{J}\)

Rounding off to three significant digits, we get:

\(E \approx 3.98 \times 10^{-19} \, \text{J}\)

However, according to the given options, the closest and most accurate value available is:

• \(3.97 \times 10^{-19} \, \text{J}\)

Thus, the correct answer is:

\(3.97 \times 10^{-19} \, \text{J}\)