Question

Calculate the energy in joule corresponding to light of wavelength 45 nm (Planck's constant, $h=6.63\times10^{-34}$ Js; speed of light, $c=3\times 10^{8}$.

• A. $6.67\times10^{15}$
• B. $6.67\times10^{11}$
• C. $6.63\times10^{-15}$
• D. $4.42\times10^{-18}$

Answer 1

The Correct Option is D

To calculate the energy corresponding to light of a given wavelength, we use the formula that relates energy, frequency, and wavelength:

E = h \cdot f

where E is the energy, h is the Planck's constant, and f is the frequency. The frequency can be calculated from the wavelength using the speed of light:

f = \frac{c}{\lambda}

where c is the speed of light, and \lambda is the wavelength.

1. Substitute the given values into the frequency formula:
   • Wavelength \lambda = 45 \, \text{nm} = 45 \times 10^{-9} \, \text{m}
   • Speed of light c = 3 \times 10^{8} \, \text{m/s}
2. Calculate frequency:
   • f = \frac{3 \times 10^{8}}{45 \times 10^{-9}} \, \text{Hz}
   • f = 6.67 \times 10^{15} \, \text{Hz}
3. Now use the value of frequency in the energy formula:
   • Planck's constant h = 6.63 \times 10^{-34} \, \text{Js}
4. Calculate energy:
   • E = 6.63 \times 10^{-34} \times 6.67 \times 10^{15}
   • E = 4.42 \times 10^{-18} \, \text{J}

Hence, the energy corresponding to the light of wavelength 45 nm is 4.42 \times 10^{-18} \, \text{J}.