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Chapter 7: Problem 40

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 \(25 \mathrm{~nm} ?\)

Short Answer

Expert verified
The energy of a single UV photon with a wavelength of \(25 nm\) is approximately \(7.97 × 10^{-19} J\), and the energy of a mole of UV photons is approximately \(4.80 × 10^5 J\).

Step by step solution

01

Convert the wavelength to meters

First, we need to convert the wavelength from nanometers (nm) to meters (m) since the other constants are in SI units. We know that 1 nm is equal to 1 × 10^-9 m. So, we can convert the given wavelength as follows: \( \lambda = 25 ~nm * \frac{1 × 10^{-9} ~m}{1 ~nm} = 25 × 10^{-9} ~m \)
02

Calculate the energy of a single photon

Now, we can plug in the values for Planck's constant (h), the speed of light (c), and the wavelength (λ) into the equation E = h * (c / λ) to find the energy of a single photon. Planck's constant (h) = 6.626 × 10^-34 Js Speed of light (c) = 3.00 × 10^8 m/s \( E = 6.626 × 10^{-34} ~Js * \frac{3.00 × 10^8 ~m/s}{25 × 10^{-9} ~m} \) Solve for E: \( E ≈ 7.97 × 10^{-19} ~J \) So, the energy of a single UV photon is approximately 7.97 × 10^-19 J.
03

Calculate the energy of a mole of photons

Now, we will find the energy of a mole of photons by multiplying the energy of a single photon by Avogadro's number (6.022 x 10^23). \( Energy~of~a~mole~of~photons = E × Avogadro's~number \) \( Energy~of~a~mole~of~photons = 7.97 × 10^{-19} ~J × 6.022 × 10^{23}~photon^{-1} \) Solve for the total energy: \( Energy~of~a~mole~of~photons ≈ 4.80 × 10^5~J \) So, the energy of a mole of UV photons is approximately 4.80 × 10^5 J.

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Most popular questions from this chapter

The first-row transition metals from chromium through zinc all have some biologic function in the human body. How many unpaired electrons are present in each of these first-row transition metals in the ground state?

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Write the expected ground-state electron configuration for each of the following. a. the lightest halogen atom b. the alkali metal with only \(2 p\) and \(3 p\) electrons c. the Group \(3 \mathrm{~A}\) element in the same period as \(\mathrm{Sn}\) d. the nonmetallic elements in Group \(4 \mathrm{~A}\)

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