Answer: 1.274 * 10^ -7 meter (same as 127.4 nanometers
Explanation:
It's given that the energy
required to break the N N triple bond is 945 * 10^3 joules per mole.
One mole contains 6.02 * 10^ 23 molecules, so the energy required per molecule
= 945 * 10^3 / 6.023 * 10^23, or 1.56 * 10^-18 joules.
Then we need a photon whose energy (E) is at least that amount.
The energy E of a photon is related to its frequency f by PLANCK'S EQUATUON,
E = hf,
where h is Planck's constant (6.625 * 10^-34 joule-sec)
and the wavelength w is inversely proportional to the frequency by w = c/f, where c is the speed of light, 2.998 * 10^8 meters per sec.
If h & c are both constants, their product hc is constant, so we can say E = hc/w,
or if we know E and want to find w, a little algebra gives: w = hc/E.
The product hc = 1.9875 * 10^-25 joule-meters,
so w = 1.9875 * 10^-25 / 1.56 * 10^-18, or 1.274 * 10^ -7 meter (same as 127.4 nanometers
