# The line spectrum for element X includes a band of green light of wavelength 522 nm. This band corresponds to what energy transition within an atom of element X? Let Planck’s constant h = 4.136 × 10−15 eV ∙ s, and the speed of light c = 3.00 × 108 m/s.

May 25, 2017

decrease of $2.38$ $\text{e V}$

#### Explanation:

Let's substitute the value of $h$ into the Planck equation $E = h f$:

Rightarrow E = (4.136 times 10^(- 15) $\text{e V}$ $\cdot$ "s") $\times f$

Then, let's substitute the definition of $f$, $f = \frac{c}{\lambda}$, into the above equation:

Rightarrow E = (4.136 times 10^(- 15) $\text{e V}$ $\cdot$ "s") $\times \frac{c}{\lambda}$

Let's substitute the values of $c$ and $\lambda$ into the equation:

Rightarrow E = (4.136 times 10^(- 15) $\text{e V}$ $\cdot$ "s") times frac(3.00 times 10^(8) " m s"^(- 1))(522 " nm")

Rightarrow E = (4.136 times 10^(- 15) $\text{e V}$ $\cdot$ "s") times frac(3.00 times 10^(8) " m s"^(- 1))(5.22 times 10^(- 7) " m")

Rightarrow E = frac(1.2408 times 10^(- 6) " e V" cdot "m")(5.22 times 10^(- 7) " m")

$R i g h t a r r o w E = 2.337$ $\text{e V}$

$\therefore E = 2.38$ $\text{e V}$

Therefore, this band corresponds to a decrease of $2.38$ $\text{e V}$.