Question

Most of the damage to DNA caused by x-rays occurs when they interact with water, knocking one of the electrons loose and creating a free radical. The energy required to do this is approximately 300 kJ/mole. If a stray photon is moving at the speed of light, estimate the wavelength(s) of electromagnetic radiation needed to create a free radical.

Answer 1

Assuming that one photon is completely absorbed and knocks off one electron in the process,

Energy of photon = Energy required to release one electron.

To create one more of electrons, 300kJ is required.

To create one electron, energy required will be

$E= \frac{300kJ}{N}$

where = avogadro number = 6.023 x10²³

$E= \frac{300 \times 10^{3}}{6.023 \times 10^{23}}= 4.98 \times 10^{-19} J$

But this should be equal to energy of the photon which is

$\frac{hc}{\lambda}$

where $\lambda$ is the wavelength of radiation

$\frac{hc}{\lambda}= 4.98 \times 10^{-19}$

$\lambda= \frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{4.98 \times 10^{-19}}= 4 \times 10^{-7} m = 400 nm$

Wavelength of 400nm is needed to create a free radical.