What is the wavelength of photons that have molar energy of 515 kJ/mol? (c = 3.00 × 10⁸ m/s,h = 6.63 × 10^-34 J · s,N_A = 6.02 × 10²³ mol^-1) A)1.29 × 10⁶nm B)8.55 × 10^-10nm C)233 nm D)3.86 × 10^-22nm E)2.33 × 10⁵nm

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Quizplus · Accepted Answer

To find the wavelength ($\lambda$) of photons with a given molar energy (E), we use the equation $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant and $c$ is the speed of light. However, since the energy given is per mole, we first convert it to energy per photon by dividing by Avogadro's number ($N_A$). Thus, $E_{\text{photon}} = \frac{515 \times 10^3 \text{ J/mol}}{6.02 \times 10^{23} \text{ mol}^{-1}}$. Then, rearrange the equation to solve for $\lambda$: $\lambda = \frac{hc}{E_{\text{photon}}}$. Plugging in the values ($h = 6.63 \times 10^{-34} \text{ J·s}$, $c = 3.00 \times 10^8 \text{ m/s}$, and $E_{\text{photon}}$ from the calculation), we find $\lambda$ in meters, which can be converted to nm (1 m = $10^9$ nm). The calculation yields a wavelength close to 233 nm.

What Is the Wavelength of Photons That Have Molar Energy