Please show calculations In photosynthesis bacteria and plants absorb radiation

Question

Please show calculations

In photosynthesis bacteria and plants absorb radiation from light and use it to generate Adenosine Triphosphate (ATP) from Adenosine diphosphate (ADP) via the reaction below: ADP + P_i right arrow ATP Some photosynthetic bacteria can light in the near-infrared region of the electromagnetic spectrum (700nm - 2500nm). Given that converting ADP to ATP requires approximately 30.5 kJ/mol of energy. Calculate how many moles of photons having a wavelength of 2450 nm are required to convert 1 moles of ADP to ATP. 0.45 moles 0.34 moles 0.75 moles 0.62 moles

Explanation / Answer

we know that

E = hc / wavelength

this is for one photon

consider n moles of photon

number of photons = n x avagadro number

number of photons = n x 6.023 x 10^23

then

energy = n x 6.023 x 10^23 x h x c / lamda

given

energy = 30.5 x 1000

h = plancks constant = 6.626 x 10-34

c = speed of light = 3 x 10^8

lamda = wavelength = 2450 x 10-9

so

using these values

we get

30.5 x 1000 = n x 6.023 x 10^23 x 6.626 x 10-34 x 3 x 10^8 / 2450 x 10-9

n = 0.624

so

0.624 moles of photoons are required

so

the answer is d) 0.62 moles

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