Question

ATP is the most common form of energy storage in biological organisms, and ATP + H₂O ® 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 = 3.0x10⁸ m/sec, and w = wavelength of light in meters (m). The energy in one mole of photons is (6.02x10²³/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.        2.64x10¹⁶ 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 10²³ 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 10²³ mol^-1) (1.58 x10^-34 cal. sec) (3 x 10⁸ m/s) / (650 x10^-9 m)

= 0.0439 x 10⁶ 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.