Question

A mole of yellow photons of wavelength 527 nm has __________ kj of energy.

Answer 1

227kj Because The first thing to do here is to calculate the energy of a single photon of wavelength equal to
527 nm
, then use Avogadro's number to scale this up to the energy of a mole of such photons.

Answer 2

Step-by-step explanation:

It is known that relation between energy and wavelength is as follows.

E =
`(hc)/(\lambda)`

where, h = plank's constant =
`6.626 * 10^(-34)`

c = speed of light =
`3 * 10^(8) m/s^(2)`

`\lambda` = wavelength

Convert nm into m as follows.

`527 nm * (1 * 10^(-9) m)/(1 nm)`

=
`527 * 10^(-9)` m

Therefore, calculate the energy as follows.

E =
`(hc)/(\lambda)`

=
`(6.626 * 10^(-34) * 3 * 10^(8) m/s^(2))/(527 * 10^(-9))`

=
`0.037719 * 10^(-17)` J

Hence, energy of the yellow light is
`0.037719 * 10^(-17)` J.

Now, calculate the moles of yellow light as follows.

`0.037719 * 10^(-17) * 6.022 * 10^(23)`

=
`0.227144 * 10^(6)` J

= 227144 J

or, = 227.14 kJ (as 1 kJ = 1000 J)

Thus, we can conclude that a mole of yellow photons of wavelength 527 nm has 227.14 kJ of energy.