Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because they carry enough energy to break bonds within the molecules. a carbon-carbon bond requires 348 kj/mol to break.

what is the longest wavelength of radiation with enough energy to break carbon-carbon bonds?

Longest wavelength = 343.7 nm

In this question we need to first use the concept of energy of a photon.

Energy of a photon, E, is given by the formula, E = hf, where h is the plank's constant, f is the frequency.

But since, f is given by dividing speed, c, by wavelength, λ, then;

E = hc/λ

We are given 348 kJ/mol required to break carbon-carbon bonds.

We know that; 1 mole of bonds = 6.022 × 10^23 bonds.

We are required to find the longest wavelength with enough energy to break the C-C bonds.

This can be worked out in simple steps:

Step 1:  Energy required to break one bond (kJ/bond)

1 mole of bonds = 6.022 × 10^23 bonds.

Therefore;

348 kJ = 6.022 × 10^23 bonds.

Thus;

1 bond = 348 kJ ÷ 6.022 × 10^23 bonds.

           =  5.778 x 10^-22 kJ

But; 1000 joules = 1 kJ

Hence; energy per bond =  5.778 x 10^-19 Joules

Step 2: Energy per photon

Breaking one bond requires energy equivalent to energy of a photon.

Therefore;

1 photon = 5.778 x 10^-19 Joules

              = 5.778 x 10^-19 J/photon

Step 3: Calculating the wavelength

From the equation of energy of a photon;

E = hc/λ

h is the plank's constant = 6.626 × 10^-34 J/s

c is the speed of light in vacuum = 2.9998 × 10^8 m/s

E is the energy of a photon =  5.778 x 10^-19 Joules

Therefore, making λ (wavelength) the subject;

       = 3.437 x 10^-7 m

But; 1 nm = 10^-9 m

Thus;

wavelength = 343.7 nm

Therefore, the longest wavelength of the radiation will be 343.7 nm

african americans demonstrated their newly found freedom by relocating often in search of relatives whom they had been separated from during slavery. others established schools to educate freed people and they built institutions such as churches and political organizations to advocate for their rights.

answer : (a) volume of the gas = 8.67 ×   l

                (b) second virial coefficient b = -1.21226 l/mole

solution :   given,     t = 300k

                                p = 20atm

                                z = 0.86

                                n = 8.2 mmoles = 8.2 × moles

                                r =   0.082 l atm/k/mol

        find,     (a) volume of gas   and (b) second virial coefficient b at 300k.

formula used :            

                          and            

(a)            

                    = \times 0.082\times 300}{20}[/tex]

                    = 8.67 ×   l

(b)      

                    = (0.00867-1) × 8.659

                    = - 8.5839 l/mole