Calculating the Energy of a Light Ray with Wavelength of 400 ?: Joules and Electronvolts
When working with light waves, one of the important aspects to consider is the energy associated with a specific wavelength. In this article, we will explore how to calculate the energy of a light ray with a wavelength of 400 ?. We will cover the relationship between the wavelength and energy using the equation ( E frac{hc}{lambda} ), where ( h ) is Planck's constant, ( c ) is the speed of light, and ( lambda ) is the wavelength.
Understanding the Relationship Between Wavelength and Energy
The energy (( E )) of a light wave can be determined using the equation ( E frac{hc}{lambda} ). This equation links the energy to the wavelength through the fundamental constants of the universe: Planck's constant (( h )) and the speed of light (( c )).
Step-by-Step Calculation
To calculate the energy of a light ray with a wavelength of 400 ? (Angstrom units), follow these steps:
Identify the Constants: Planck's constant (( h )) is approximately ( 6.626 times 10^{-34} ) Joule seconds, and the speed of light (( c )) is approximately ( 3 times 10^8 ) meters per second. Note that 1 ? ( 10^{-10} ) meters. Convert Wavelength to Meters: The given wavelength is 400 ?. Therefore, ( lambda 400 times 10^{-10} ) meters. Apply the Equation: Substitute the values into the equation ( E frac{hc}{lambda} ).Performing the Calculation
The energy in Joules will be:
[text{Energy} frac{6.626 times 10^{-34} times 3 times 10^8}{400 times 10^{-10}} text{Joules}]First, simplify the denominator:
[text{Energy} frac{19.878 times 10^{-26}}{400 times 10^{-10}} text{Joules}]Now, perform the division:
[text{Energy} frac{19.878 times 10^{-26}}{4 times 10^{-8}} text{Joules}]Calculate the numerator and denominator separately:
[text{Energy} 4.9695 times 10^{-18} text{Joules}]Rounding to an appropriate number of significant figures, we get:
[text{Energy} 4.97 times 10^{-18} text{Joules}]Next, convert joules to electronvolts (eV). The conversion factor is ( 1 text{ eV} 1.6 times 10^{-19} text{ Joules} ). Therefore:
[text{Energy in eV} frac{4.97 times 10^{-18}}{1.6 times 10^{-19}} text{ eV}]Perform the division:
[text{Energy in eV} 31.06 text{ eV}]Hence, the energy of a light ray with a wavelength of 400 ? is approximately 4.97 x 10^-18 Joules or 31.06 eV.
Conclusion
Understanding the energy of a light ray with a specific wavelength is crucial in various fields of physics and engineering. By utilizing the fundamental constants and the equation ( E frac{hc}{lambda} ), one can determine the energy with precision. This method offers a practical approach to converting between energy units such as Joules and Electronvolts, making it easier to apply in experimental and theoretical contexts.