Each photon of light has energy hv, where h is Plank’s constant (1.58X10-37 kcal
ID: 1597805 • Letter: E
Question
Each photon of light has energy hv, where h is Plank’s constant (1.58X10-37 kcal sec/photon) and v is the frequency in sec-1. The frequency of light is equal to c/, where c is the speed of light (3.0X1017 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 X 1023 photons/mole) at 400 nm (violet light), 680 nm (red light), and at 800 nm (infrared light).
B.Bright sunlight strikes Earth at the rate of about 0.3 kcal/sec per square meter. Assuming for the sake of calculation that sunlight consists of monochromatic light of wavelength 680 nm, how many seconds does it take to a amole of photons to strike a square meter?
C.Assuming that it takes 8 photons to fix one molecule of CO2 as carbohydrate under optimal conditions, 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.
D.If it takes 112 kcal/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 8 photons of red light (680 nm) are required to fix one molecule of CO2.
Explanation / Answer
a)
if
lambda=400 nm
energy, E=N*h*c/lambda
=6.022*10^23*6.626*10^-34*3*10^8/(400*10^-9)
=2.9*10^5 J/mol ------->
and
lambda=680 nm
energy, E=N*h*c/lambda
=6.022*10^23*6.626*10^-34*3*10^8/(680*10^-9)
=1.76*10^5 J/mol ------->
and
lambda=800 nm
energy, E=N*h*c/lambda
=6.022*10^23*6.626*10^-34*3*10^8/(800*10^-9)
=1.5*10^5 J/mol ------->
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