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Textbook Solutions for Molecular Biology of the Cell

Chapter 14 Problem 14-11

Question

How much energy is available in visible light? How much energy does sunlight deliver to Earth? How efficient are plants at converting light energy into chemical energy? The answers to these questions provide an important backdrop to the subject of photosynthesis. Each quantum or photon of light has energy hv, where h is Plancks constant (6.6 1037 kJ sec/photon) and v is the frequency in sec1. The frequency of light is equal to c/, where c is the speed of light (3.0 1017 nm/ sec) and is the wavelength in nm. Thus, the energy (E) of a photon is E = hv = hc/ A. Calculate the energy of a mole of photons (6 1023 photons/mole) at 400 nm (violet light), at 680 nm (red light), and at 800 nm (near-infrared light). B. Bright sunlight strikes Earth at the rate of about 1.3 kJ/sec per square meter. Assuming for the sake of calculation that sunlight consists of monochromatic light of wavelength 680 nm, how many seconds would it take for a mole of photons to strike a square meter? C. Assuming that it takes eight photons to fix one molecule of CO2 as carbohydrate under optimal conditions (810 photons is the currently accepted value), calculate how long it would take a tomato plant with a leaf area of 1 square meter to make a mole of glucose from CO2. Assume that photons strike the leaf at the rate calculated above and, furthermore, that all the photons are absorbed and used to fix CO2. Figure p14.04/14.07 p14-31/14-47 actin filament direction of rotation inner membrane matrix (A) (B) 0 1 2 3 4 5 0 20 40 60 80 100 revolutions time (seconds) Figure Q142 Experimental set-up for observing rotation of the subunit of ATP synthase ( 1410). (A) The immobilized 33 complex. The subunits are anchored to a solid support and a fluorescent actin filament is attached to the subunit. (B) Stepwise revolution of the actin filament. The indicated trace is a typical example from one experiment. The inset shows the positions in the revolution at which the actin filament pauses. (B, from R. Yasuda et al., Cell 93:11171124, 1998. With permission from Elsevier.) 811 Figure p14.23/14.15 p14.109/14.80 REFERENCES D. If it takes 468 kJ/mole to fix a mole of CO2 into carbohydrate, what is the efficiency of conversion of light energy into chemical energy after photon capture? Assume again that eight photons of red light (680 nm) are required to fix one molecule of CO2.

Solution

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The first step in solving 14 problem number 11 trying to solve the problem we have to refer to the textbook question: How much energy is available in visible light? How much energy does sunlight deliver to Earth? How efficient are plants at converting light energy into chemical energy? The answers to these questions provide an important backdrop to the subject of photosynthesis. Each quantum or photon of light has energy hv, where h is Plancks constant (6.6 1037 kJ sec/photon) and v is the frequency in sec1. The frequency of light is equal to c/, where c is the speed of light (3.0 1017 nm/ sec) and is the wavelength in nm. Thus, the energy (E) of a photon is E = hv = hc/ A. Calculate the energy of a mole of photons (6 1023 photons/mole) at 400 nm (violet light), at 680 nm (red light), and at 800 nm (near-infrared light). B. Bright sunlight strikes Earth at the rate of about 1.3 kJ/sec per square meter. Assuming for the sake of calculation that sunlight consists of monochromatic light of wavelength 680 nm, how many seconds would it take for a mole of photons to strike a square meter? C. Assuming that it takes eight photons to fix one molecule of CO2 as carbohydrate under optimal conditions (810 photons is the currently accepted value), calculate how long it would take a tomato plant with a leaf area of 1 square meter to make a mole of glucose from CO2. Assume that photons strike the leaf at the rate calculated above and, furthermore, that all the photons are absorbed and used to fix CO2. Figure p14.04/14.07 p14-31/14-47 actin filament direction of rotation inner membrane matrix (A) (B) 0 1 2 3 4 5 0 20 40 60 80 100 revolutions time (seconds) Figure Q142 Experimental set-up for observing rotation of the subunit of ATP synthase ( 1410). (A) The immobilized 33 complex. The subunits are anchored to a solid support and a fluorescent actin filament is attached to the subunit. (B) Stepwise revolution of the actin filament. The indicated trace is a typical example from one experiment. The inset shows the positions in the revolution at which the actin filament pauses. (B, from R. Yasuda et al., Cell 93:11171124, 1998. With permission from Elsevier.) 811 Figure p14.23/14.15 p14.109/14.80 REFERENCES D. If it takes 468 kJ/mole to fix a mole of CO2 into carbohydrate, what is the efficiency of conversion of light energy into chemical energy after photon capture? Assume again that eight photons of red light (680 nm) are required to fix one molecule of CO2.
From the textbook chapter DNA, Chromosomes, and Genomes you will find a few key concepts needed to solve this.

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Title Molecular Biology of the Cell 6 
Author Bruce Alberts
ISBN 9780815344322

How much energy is available in visible light How much energy does sunlight deliver to

Chapter 14 textbook questions

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