What is the wavelength, in nm, of light with an energy content of (1.35x10^3 kJ/mol)?

Thank you!!!

E = hc/wavelength

E = must be in J/photon; therefore, 1350000/6.02E23 = E
Then fill in h, c and solve for wavelength and convert to nm.

To find the wavelength of light with a given energy content, you can use the equation:

E = hc/λ

Where:
E is the energy (1.35x10^3 kJ/mol, which needs to be converted to J/molecule)
h is Planck's constant (6.62607015x10^-34 J·s)
c is the speed of light (2.998x10^8 m/s)
λ is the wavelength (unknown)

Let's start by converting the energy from kJ/mol to J/molecule.

1 kJ = 1x10^3 J
1 mol = 6.02214076x10^23 molecules

So, the energy content in J/molecule is:

E = (1.35x10^3 kJ/mol) x (1x10^3 J/1 kJ) / (6.02214076x10^23 molecules/1 mol)

E = 2.24x10^-21 J/molecule

Now, substitute the values into the equation and solve for λ.

2.24x10^-21 J/molecule = (6.62607015x10^-34 J·s) x (2.998x10^8 m/s) / λ

Rearrange the equation to find λ:

λ = (6.62607015x10^-34 J·s) x (2.998x10^8 m/s) / (2.24x10^-21 J/molecule)

Calculating this, we find:

λ ≈ 8.85x10^-7 m

Finally, convert meters to nanometers (nm):

λ = 8.85x10^-7 m x (1x10^9 nm/1 m)

λ ≈ 885 nm

Therefore, the wavelength of light with an energy content of 1.35x10^3 kJ/mol is approximately 885 nm.

To find the wavelength of light with a given energy content, you can use the equation:

\[E = \frac{{hc}}{{\lambda}}\]

Where:
- E is the energy content of the light,
- h is Planck's constant (6.62607015 × 10^(-34) J·s),
- c is the speed of light in a vacuum (2.998 × 10^8 m/s),
- λ is the wavelength of the light.

First, convert the energy content of the light from kJ/mol to J/molecule by multiplying by the conversion factor:
\[1.35 × 10^3 \, \text{kJ/mol} = 1.35 × 10^3 \times 10^3 \, \text{J/mol} = 1.35 × 10^6 \, \text{J/mol}\]

To calculate the number of molecules from the given energy content, you need to know the Avogadro's constant, which is approximately \(6.022 × 10^{23}\) mol^(-1). Since the question does not provide the number of molecules, we will assume it to be one. Now we can find the energy per molecule:

\[\text{Energy per molecule} = \frac{{1.35 × 10^6 \, \text{J/mol}}}{{6.022 × 10^{23} \, \text{mol}^{-1}}}\]

Next, substitute the values into the equation for energy, \(E = \frac{{hc}}{{\lambda}}\):

\[\frac{{1.35 × 10^6 \, \text{J}}}{{6.022 × 10^{23}}} = \frac{{(6.62607015 × 10^{-34} \, \text{J·s})(2.998 × 10^8 \, \text{m/s})}}{{\lambda}}\]

Rearrange the equation to solve for the wavelength, λ:

\[\lambda = \frac{{(6.62607015 × 10^{-34} \, \text{J·s})(2.998 × 10^8 \, \text{m/s})}}{{\frac{{1.35 × 10^6 \, \text{J}}}{{6.022 × 10^{23}}}}}\]

Now, you can solve for the wavelength, λ, using the given values:

\[\lambda = \frac{{(6.62607015 × 10^{-34} \, \text{J·s})(2.998 × 10^8 \, \text{m/s})}}{{\frac{{1.35 × 10^6 \, \text{J}}}{{6.022 × 10^{23}}}}}\]

Finally, calculate the wavelength using the calculated values. The resulting wavelength will be in meters (m). To convert it to nanometers (nm), multiply by 10^9:

\[\lambda = \left(\frac{{(6.62607015 × 10^{-34} \, \text{J·s})(2.998 × 10^8 \, \text{m/s})}}{{\frac{{1.35 × 10^6 \, \text{J}}}{{6.022 × 10^{23}}}}}\right) \times 10^9\]

Evaluating this expression will give you the wavelength of light in nanometers (nm).