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Chapter 7: Problem 48

A photon of ultraviolet (UV) light possesses enough energy to mutate a strand of human DNA. What is the energy of a single UV photon and a mole of UV photons having a wavelength of 25 nm?

Short Answer

Expert verified
The energy of a single UV photon with a wavelength of 25 nm is \(E = \frac{6.626 \times 10^{-34} Js \cdot 2.998 \times 10^8 m/s}{25 \times 10^{-9} m} = 7.97 \times 10^{-18} J\). To find the energy of a mole of UV photons, we multiply the energy of a single photon by Avogadro's number: \(Energy\_of\_mole\_of\_photons = E \times 6.022 \times 10^{23} photons/mole = 7.97 \times 10^{-18} J \times 6.022 \times 10^{23} photons/mole = 4.80 \times 10^6 J/mole\). Therefore, the energy of a single UV photon is \(7.97 \times 10^{-18} J\) and the energy of a mole of UV photons is \(4.80 \times 10^6 J/mole\).

Step by step solution

01

Calculate the energy of a single photon

To calculate the energy of a single photon, we'll use Planck's equation: E = h * c / λ Where: E = energy of a single photon, h = Planck's constant (6.626 × 10^-34 Js), c = speed of light (2.998 × 10^8 m/s), and λ = wavelength of the UV photons (25 nm which is equal to 25 x 10^-9 m) E = (6.626 × 10^-34 Js) * (2.998 × 10^8 m/s) / (25 × 10^-9 m)
02

Find the energy of a mole of photons

To find the energy of a mole of photons, we'll multiply the energy of a single photon by Avogadro's number: Energy of a mole of photons = E_single_photon × Avogadro's_number Let N_A = Avogadro's number (6.022 × 10^23 photons/mole) Energy_of_mole_of_photons = E × N_A Now, let's compute the energy of a single photon and a mole of photons.

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