Question

A particular color of light has a wavelength of 663 nm. What is the energy possessed by the light? 
(Planck’s constant $h = 6.63 \times 10^{-34}$ J·s; Velocity of light $c = 3 \times 10^8$ m/s)

• A. $6.63 \times 10^{-19}$ J
• B. $6.63 \times 10^{-20}$ J
• C. $1.5 \times 10^{-19}$ J
• D. $3.0 \times 10^{-20}$ J
• E. $3.0 \times 10^{-19}$ J

Hint:

Photon energy is inversely proportional to wavelength: shorter wavelengths have higher energy.

Answer 1

Answer: (E)

Step 1: The energy of a photon is given by: \[ E = \frac{hc}{\lambda} \] where: - $h = 6.63 \times 10^{-34}$ J·s - $c = 3 \times 10^8$ m/s - $\lambda = 663$ nm = $663 \times 10^{-9}$ m 
Step 2: Substituting values: \[ E = \frac{(6.63 \times 10^{-34}) \times (3 \times 10^8)}{663 \times 10^{-9}} \] Step 3: Calculating the numerator: \[ (6.63 \times 10^{-34}) \times (3 \times 10^8) = 1.989 \times 10^{-25} \] Step 4: Dividing by the denominator: \[ E = \frac{1.989 \times 10^{-25}}{663 \times 10^{-9}} \] \[ E = 3.0 \times 10^{-19} { J} \] Step 5: Therefore, the correct answer is (E).