Question

The wavelength of a photon is 500 nm. Calculate its energy. (Planck’s constant \( h = 6.63 \times 10^{-34} \, \text{J·s} \), speed of light \( c = 3 \times 10^8 \, \text{m/s} \))

• A. \( 3.98 \times 10^{-19} \, \text{J} \)
• B. \( 4.14 \times 10^{-19} \, \text{J} \)
• C. \( 5.24 \times 10^{-19} \, \text{J} \)
• D. \( 2.48 \times 10^{-19} \, \text{J} \)

Hint:

Use $E = \frac{hc}{\lambda}$ to calculate photon energy. Convert wavelength to meters before substitution.

Answer 1

The Correct Option is A

Photon energy is given by: \[ E = \frac{hc}{\lambda} \] Given: \[ h = 6.63 \times 10^{-34}, \quad c = 3 \times 10^8, \quad \lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} \] Substitute: \[ E = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{500 \times 10^{-9}} = \frac{1.989 \times 10^{-25}}{5 \times 10^{-7}} = 3.978 \times 10^{-19} \, \text{J} \] \[ E \approx 3.98 \times 10^{-19} \, \text{J} \]

Answer 2

To solve the problem, we need to calculate the energy of a photon with wavelength 500 nm using Planck’s constant and the speed of light.

1. Formula for Energy of a Photon:  
The energy $E$ of a photon is given by:
$ E = \frac{hc}{\lambda} $
where
$h = 6.63 \times 10^{-34}\, \text{J·s}$ (Planck’s constant)
$c = 3 \times 10^8\, \text{m/s}$ (speed of light)
$\lambda = 500\, \text{nm} = 500 \times 10^{-9}\, \text{m}$ (wavelength)

2. Substituting the values:
$ E = \frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{500 \times 10^{-9}} $

3. Calculate the numerator and denominator:
Numerator = $6.63 \times 10^{-34} \times 3 \times 10^{8} = 1.989 \times 10^{-25}$
Denominator = $500 \times 10^{-9} = 5 \times 10^{-7}$

4. Calculate Energy:
$ E = \frac{1.989 \times 10^{-25}}{5 \times 10^{-7}} = 3.978 \times 10^{-19} \, \text{J} $

Final Answer:
The energy of the photon is $ {3.98 \times 10^{-19} \, \text{J}} $.