Question

Repeat the calculation of problem 49 for red light with wavelength 700nm.

Short answer

The total number of molecules of ATP produced will be 5N_A.

Step-by-step solution

Photoelectric effect

The photoelectric effect occurs when light shines on a metal and causes electrons to be expelled from the metal's surface. Photoemission is another name for this process, and photoelectrons are the electrons that are emitted from the metal.

Calculation of total energy

Given that, wavelength (λ) is 700nm at room temperature and under neutral pH.

According to photoelectric equation,

$E=\frac{hc}{\lambda }{N}_A$

Where, h = Planck’s constant, c = speed of light, and ${\text{N}}_{\text{A}}$= Avogadro’s number.

The known values are substituted.

$$\begin{gathered} \text{E}=\frac{hc}{\lambda }{N}_A \\ \text{E}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{700\times {10}^{-9}}\times 6.023\times {10}^{23} \\ {\text{E = 171.138kJ mol}}^{\text{- 1}} \end{gathered}$$

Calculation of total number of ATP molecules

According to given information, for formation of one molecule of ATP 34.5kJ energy is required.

So, number of molecules formed due to 1 mol of photons can be given by-

$n=\frac{E}{\Delta G}{N}_A$

Where,

• n is number of molecules
• E is energy of 1 mole of photons
• ΔG is energy of formation of one mole of ATP

Then,

$$\begin{gathered} n=\frac{171.138}{34.5}{N}_A \\ n=4.96 \\ n\approx 5N_A \end{gathered}$$

Hence, 5N_A molecules of ATP can be formed.