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.

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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.

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Answer 1 · 2017-05-25T20:42:18

decrease of $2.38$ $2.38$ $e V$ $"e V"$

Explanation:

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

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

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

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

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

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

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

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

$\Rightarrow E = 2.337$ $Rightarrow E = 2.337$ $e V$ $"e V"$

$therefore E = 2.38$ $"e V"$

Therefore, this band corresponds to a decrease of $2.38$ $"e V"$ .

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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.

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Explanation:

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