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

explanation:

metals have excess of electrons whereas non-metals have deficiency of electrons. thus, in order to gain stability metals easily donate their electrons to the non-metals.

for example, electronic configuration of sodium is and electronic configuration of phosphorous is .

when a phosphorous atom and sodium atom combine together then sodium will donate is extra one electron to the phosphorous atom. as a result there will be formation of ionic bond between sodium and phosphorous.

the reaction will be as follows.

there, are three sodium sodium atoms and each of them will donate its one extra electron to phosphorous atom. thus, the sub-shell of phosphorous gets completely filled.  

thus, we can conclude that electrons are transferred from atoms of sodium to atoms of phosphorous. this transfer makes the sodium atoms donate one electron and the phosphorous atoms to gain one electron. as a result, the sodium and phosphorus atoms strongly attract each other.