What is the wavelength of light (in nm) if the energy of the wave is 1.33x 10^-19 J? How do I work this problem out????
E = hc/wavelength
You know E from the problem, h is Planck's constant, c is speed of light (3E8 m/s) and you solve for wavelength.
To determine the wavelength of light, you can use the equation:
E = hc/λ
where E represents the energy of the wave, h is Planck's constant (6.626 x 10^-34 Js), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of light.
To work out the problem, you need to rearrange the equation to solve for λ.
Start by rearranging the equation as follows:
λ = hc/E
Now, substitute the given values into the equation:
λ = (6.626 x 10^-34 Js) × (3.00 x 10^8 m/s) / (1.33 x 10^-19 J)
Calculate the numerator:
(6.626 x 10^-34 Js) × (3.00 x 10^8 m/s) = 1.9888 x 10^-25 Jm
Now, divide the numerator by the denominator:
λ = 1.9888 x 10^-25 Jm / (1.33 x 10^-19 J)
Simplify:
λ = 1.9888 x 10^-25 Jm / 1.33 x 10^-19 J
λ ≈ 1.496 x 10^-6 m
To convert the wavelength from meters (m) to nanometers (nm), multiply by 10^9:
λ ≈ 1.496 x 10^-6 m × 10^9 nm/m
λ ≈ 1.496 x 10^3 nm
Therefore, the wavelength of light with an energy of 1.33 x 10^-19 J is approximately 1.496 x 10^3 nm.
To determine the wavelength of light given the energy of the wave, you can use the equation E = hc/λ, where E represents the energy of the wave, h is Planck's constant (approximately 6.626 x 10^-34 J·s), c is the speed of light in a vacuum (approximately 3.00 x 10^8 m/s), and λ represents the wavelength of light.
To work through the problem, you will need to rearrange the equation to solve for the wavelength (λ):
λ = hc/E
First, let's convert the given energy (1.33 x 10^-19 J) to joules. Since we are given the energy in joules, we don't need to perform any unit conversions:
E = 1.33 x 10^-19 J
Next, substitute the values into the equation and perform the calculation:
λ = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (1.33 x 10^-19 J)
Now, perform the multiplication to get the numerator:
λ = (1.9878 x 10^-25 J·m) / (1.33 x 10^-19 J)
Finally, divide the numerator by the denominator to obtain the wavelength value:
λ ≈ 1.495 x 10^-6 meters
To convert the wavelength from meters to nanometers, multiply by 10^9:
λ ≈ 1.495 x 10^-6 meters * 10^9 nm/m = 1.495 x 10^3 nm
So, the wavelength of light with an energy of 1.33 x 10^-19 J is approximately 1.495 x 10^3 nm.