Question

Calculate the energy of a photon (in Joules) with a wavelength of \(500\ \text{nm}\), given \(h = 6.6 \times 10^{-34}\ \text{Js}\).

• A. \(3.96 \times 10^{-19}\ \text{J}\)
• B. \(1.98 \times 10^{-19}\ \text{J}\)
• C. \(5.00 \times 10^{-19}\ \text{J}\)
• D. \(7.92 \times 10^{-19}\ \text{J}\)

Hint:

To quickly estimate photon energy, remember the formula \(E = \frac{hc}{\lambda}\). Shorter wavelengths correspond to {higher photon energy}.

Answer 1

The Correct Option is A

Concept: The energy of a photon is given by the Planck–Einstein relation: \[ E = \frac{hc}{\lambda} \] where:

• \(E\) = Energy of the photon
• \(h\) = Planck’s constant \(= 6.6 \times 10^{-34}\ \text{Js}\)
• \(c\) = Speed of light \(= 3 \times 10^8\ \text{m/s}\)
• \(\lambda\) = Wavelength of the photon

Before substituting, convert the wavelength from nanometers to meters: \[ 500\ \text{nm} = 500 \times 10^{-9}\ \text{m} = 5 \times 10^{-7}\ \text{m} \]
Step 1: Substitute the values into the photon energy formula.
\[ E = \frac{(6.6 \times 10^{-34})(3 \times 10^8)}{5 \times 10^{-7}} \]
Step 2: Simplify the numerator.
\[ 6.6 \times 3 = 19.8 \] \[ E = \frac{19.8 \times 10^{-26}}{5 \times 10^{-7}} \]
Step 3: Divide the coefficients and adjust powers of ten.
\[ E = 3.96 \times 10^{-19}\ \text{J} \] Thus, the energy of the photon is: \[ E = 3.96 \times 10^{-19}\ \text{J} \]