Question

A photon of ultraviolet (uv) light possesses enough energy to mutate a strand of human dna. what is the energy of a single uv photon and a mole of uv photons having a wavelength of 25 nm?

Answer 1

Energy of single uv photon= 7.95 x 10⁻¹⁸ J

Energy of a mole of photons=4788213 J

Explanation:

the energy of a photon is given by $E= \frac{h c}{\lambda}$

h= planck's constant=6.626 x 10⁻³⁴ Js

λ= wavelength=25 nm= 25 x 10⁻⁹ m

c= velocity of light= 3 x 10⁸ m/s

so $E= \frac{6.626\times10^{-34}(3\times10^{8})}{25\times10^{-9}}$

E=7.95 x 10⁻¹⁸ J

so energy of one photon=7.95 x 10⁻¹⁸ J

Energy of one mole of photons= 6.022 x 10²³ (7.95 x 10⁻¹⁸ J)

Energy of one mole of photons=4788213 J

Answer 2

The energy of one mole of photon is $4.78 \times 10^{6} \;\rm J$.

Given data:

The wavelength of photon is, $\lambda = 25 \;\rm nm = 25\times 10^{-9} \;\rm m$.

The energy of one photon is given as,

$E=\dfrac{hc}{\lambda}$

Here, h is the Planck's constant and c is the speed of light.

Solving as,

$E=\dfrac{6.63\times10^{-34} \times 3 \times 10^{8}}{25 \times 10^{-9}}\\E=7.956 \times 10^{-18} \;\rm J$

Now, energy of mole of photon is,

$E'=N \times E$

N is the Avogadro's number.

$E'=6.022 \times 10^{23} \times (7.956 \times 10^{-18})\\E' =4.78 \times 10^{6} \;\rm J$

Thus, the energy of one mole of photon is $4.78 \times 10^{6} \;\rm J$.

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