Ch.7 - Quantum-Mechanical Model of the Atom

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.7 - Quantum-Mechanical Model of the Atom

Problem 43

Chapter 7, Problem 43

A laser pulse with wavelength 532 nm contains 3.85 mJ of energy. How many photons are in the laser pulse?

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Calculate the energy of one photon using the equation \(E = \frac{hc}{\lambda}\), where \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)), \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)), and \(\lambda\) is the wavelength of the photon (532 nm converted to meters).

Convert the energy of the laser pulse from millijoules to joules.

Divide the total energy of the laser pulse by the energy of one photon to find the number of photons. Use the formula \(N = \frac{E_{\text{total}}}{E_{\text{photon}}}\), where \(N\) is the number of photons, \(E_{\text{total}}\) is the total energy of the pulse, and \(E_{\text{photon}}\) is the energy of one photon.

Ensure the units are consistent when performing the calculations, particularly converting nm to meters for wavelength and mJ to J for energy.

Check the calculation for accuracy by verifying the units cancel appropriately, leaving a unitless count of photons.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Photon Energy

The energy of a single photon can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. This relationship shows how the energy of photons is inversely proportional to their wavelength.

Total Energy of the Laser Pulse

The total energy of the laser pulse is given as 3.85 mJ, which can be converted to joules (1 mJ = 0.001 J). This total energy represents the cumulative energy of all the photons emitted in the pulse, and is essential for determining the number of photons present.

Calculating the Number of Photons

To find the number of photons in the laser pulse, divide the total energy of the pulse by the energy of a single photon. This calculation provides the total count of photons, illustrating the relationship between energy and the quantized nature of light.

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Textbook Question

List these types of electromagnetic radiation in order of (i) increasing frequency and (ii) decreasing energy per photon. a. gamma rays b. radio waves c. microwaves d. visible light

List these types of electromagnetic radiation in order of (ii) increasing energy per photon. a. radio waves b. microwaves c. infrared radiation d. ultraviolet radiation

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Textbook Question

A heat lamp produces 32.8 watts of power at a wavelength of 6.5 µm. How many photons are emitted per second? (1 watt = 1 J/s)

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Textbook Question

Calculate the energy of a photon of electromagnetic radiation at each of the wavelengths indicated in Problem 39. a. 632.8 nm (wavelength of red light from helium–neon laser) b. 503 nm (wavelength of maximum solar radiation) c. 0.052 nm (wavelength contained in medical X-rays)

Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm) b. visible light (500 nm) c. ultraviolet radiation (150 nm)

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Textbook Question

How much energy is contained in 1 mol of each? a. X-ray photons with a wavelength of 0.135 nm b. γ-ray photons with a wavelength of 2.15×10^–5 nm

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