Question

How many moles of ATP could be synthesised at 100% efficiency by a photosynthetic organism upon absorption of 1 einstein of red light (700 nm)

a)0.1 mole of ATP/ einstein

b)5 mole of ATP/ einstein

c)50 mole of ATP/ einstein

d)100 mole of ATP/ einstein​

Answer 1

1 Einstein of red light synthesize approx  5 moles of ATP (option (B))

Step by step explanation:

According to Einstein's  photoelectric equation

$E = \frac{h \times c}{\lambda }$                                                                     (Equation 1)

where

E =  Einstein energy of corresponding wavelength

h = plank' s constant = $6.62607004 \times 10^-^3^4 m^2 \frac {kg}{ s}$

c = speed of light = $3 \times 10^8 ms^-^1$

and λ = Wavelength  = 700 nm     (given)

So 1 Einstein of red light = $E = \frac{6.62607004 \times 10^-^3^4 \times 3 \times 10^8 }{700 \times 10^-^9 }$

It is approximately equal to 40.8 k cal

We know that 1  mole of ATP gives 7.5 kcal energy

So in 1 einstein of red light the number of moles of ATP = $\frac{40.8}{7.5}$

$\textbf{\Large = 5.44 moles of ATP}$

So (Option (b)) is correct.

Answer 2

Thus the energy is 50 ATPs / Einstein

Option (C) is correct.

Explanation:

Given data:

• Efficiency = 100 %
• Amount of light = 1 Einstein

Solution:

NA = 6.02 x 10^23

1 Einstein = energy in one mole of photons

E =  h c /λ

Energy of 1 Einstein = 6.02 x 10^23 x hc /

Energy of 1 Einstein = 28600 / 700 K cal

Energy of 1 Einstein = 40.8 K cal

No. of Einstein absorbed by 2 mole of Oxygen = 9

Energy used = 9 x 40.8 = 368 Kcal

1 ATP gives = 7.3 K cal

368 K Cal = 50.4 ATP molecules

Thus the energy is 50 ATPs / Einstein