Question

In a hypothetical element, two energy levels are separated by an energy of 282 kJmol. What wavelength of light (in nm) is involved for an electron to change between these two level?

Answer 1

Concept:

Wavelength is that the distance between identical points (adjacent crests) within the adjacent cycles of a waveform signal propagated in space or along a wire.

Given:

We are provided that two energy levels are separated by an energy of$282kJmol.$

Find:

We have to seek out the wavelength of sunshine (in nm) is involved for an electron to vary between these two level.

Solution:

Firstly, we are going to find the energy for one atom by using the formula$E=\frac{E^{\prime}}{\text{Avagadro number}}$

Where $E^{\prime}=282$ and Avagadro number$=6.022\times 10^{23}$

Now, substitute the values within the formula, we get

$\begin{aligned}E&=\frac{282}{6.022\times 10^{23}}\\ &=4.68\times 10^{-19}\end$

Further, we'll find the wavelength of the sunshine using the formula $E=\frac{hc}{\lambda}$ where $h$ is Planck's constant $h=6.626\times 10^{-34}Js$ and $c$ is that the speed of the sunshine $c=3\times 10^{8}m/s$.

Furthermore, Substutute the values, we get

$\begin{aligned}\lambda&=\frac{hc}{E}\\ &=\frac{6.626\times 10^{-34}\times 3\times 10^{8}}{4.68\times 10^{-19}}\\ &=4.248\times 10^{-7}\\ &=428\times 10^{-9}m\end$

Hence, the wavelength of sunshine is $428nm.$