Question

ATP is the most common form of energy storage in biological
organisms, and ATP + H_{2}O ® ADP + P_{i} has DG =
-7.3 kcal/mole under standard conditions and as much as DG = –12
kcal/mole in cells. A photon is the smallest packet of light that
can interact with matter. The energy E_{p} of one photon of
light depends upon its wavelength according to the formula
E_{p} = hc/w where h = Planck's constant =
1.58x10^{-34} cal sec, c = speed of light =
3.0x10^{8} m/sec, and w = wavelength of light in meters
(m). The energy in one mole of photons is
(6.02x10^{23}/mole)x(E_{p}). How many kcal of
energy are carried by one mole of photons of wavelength w = 650 nm
= 650x10^{-9} m, a wavelength of light that is strongly
absorbed by chlorophyll?

A. 43,900 kcal/mole of photons

B. 0.044 kcal/mole of photons

C.
2.64x10^{16} kcal/mole of photons

D. 43.9 kcal/mole of photons

E.
7.3x10^{-17} kcal/mole of photons

Answer #1

We know that Energy in one mole of photons is

E = Nhc/λ

N = Avogadro number = 6.023 x 10^{23}
mol^{-1}

h= planck's constant = 1.58 x10-^{34}
cal sec

c = velocity of light = 3 x 10 ^{8} m/s

Given that λ = wavelength
= 650 x10^{-9}
m

E = Nhc/λ

E = Nhc/λ

= (6.023 x 10^{23} mol^{-1}) (1.58
x10^{-34} cal. sec) (3 x 10^{8} m/s) / (650
x10^{-9} m)

= 0.0439 x 10^{6}
cal/ mole of photons

= 43.9 kcal/ mole of photons

E = 43.9 kcal/ mole of photons

Therefore,

Energy carried by one mole of photons of wavelength 650 nm is 43.9 kcal.

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