Find the wavelength (in nm) of a photon whose energy is 5.90 x 10-19 J.
I understand that I have to use this equation to figure out the problem E=nhf, I just keep getting the wrong answer. Which is 33.68 nm
E=hf=h c/lambda
lambda=hc/E=6.6E-34*3E8/5.9E-19
=3.3E-7m=330nm
you do it more accurately
Thanks It deffinatly helped some. I also realised I was downsizing the number to much.
To find the wavelength (λ) of a photon with energy (E) in joules, you can use the equation:
E = hf
Where:
E = Energy of the photon
h = Planck's constant (6.62607015 × 10^(-34) J⋅s)
f = frequency of the photon
Rearranging the equation, we have:
f = E / h
Now, since the speed of light (c) is related to the wavelength (λ) and frequency (f) by the equation:
c = λf
We can express the frequency (f) as:
f = c / λ
Substituting this expression for frequency back into the rearranged equation from earlier:
E / h = c / λ
Rearranging the equation to solve for the wavelength (λ):
λ = (hc) / E
Now, substitute the given values:
E = 5.90 × 10^(-19) J
h = 6.62607015 × 10^(-34) J⋅s
c = speed of light = 2.998 × 10^8 m/s
λ = [(6.62607015 × 10^(-34) J⋅s) × (2.998 × 10^8 m/s)] / (5.90 × 10^(-19) J)
Calculating the value, we get:
λ ≈ 3.363 nm
Therefore, the wavelength of the photon with an energy of 5.90 × 10^(-19) J is approximately 3.363 nm.
To find the wavelength of a photon with a given energy, you can use the equation E = hf, where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), and f is the frequency of the photon.
Since you already have the energy of the photon (5.90 x 10^-19 J), you need to rearrange the equation to solve for the frequency.
E = hf
Divide both sides of the equation by h:
f = E / h
Now, you can substitute the given values to find the frequency:
f = (5.90 x 10^-19 J) / (6.626 x 10^-34 J·s)
Calculating this, you get:
f = 8.90 x 10^14 Hz
Now that you have the frequency, you can determine the wavelength using the equation c = λf, where c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength, and f is the frequency.
Rearranging the equation, you get:
λ = c / f
Substitute the values:
λ = (3.00 x 10^8 m/s) / (8.90 x 10^14 Hz)
Converting the result to nm (nanometers), you get the wavelength:
λ = 337 nm
So, the correct wavelength of a photon with an energy of 5.90 x 10^-19 J is 337 nm, not 33.68 nm. Double-check your calculations to find where the mistake might have occurred.