 # Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. Determine the wavelength of light that is associated with this transition. Will the light be absorbed or emitted? The main objective of this question is to find the wavelength of light which is related to the electron transition when it jumps from lower energy state to higher level of energy.This question uses the concept of the wavelength of light. The distance between the two subsequent crests or troughs is known as the light wavelength. It is denoted by $\lambda$.  Light has a wavelength that varies from 400 nm in the violet region to 700 nm in the red region of the spectrum.

We have to find the wavelength of light which is related to the electron transition when it jumps from lower energy state to higher level of energy.

We know that energy change is:

$\Delta E \space = \space 1.09 \space \times 10^{-19} \times j$

Planck constant  $h$ is $6.626 \space \times 10^{-34} js$.

And the speed of light is $2.998 \space \times 10^8 \frac{m}{s}$.

Now calculating the wavelength of light:

$\lambda \space = \space \frac{hc}{\Delta E}$

By putting values, we get:

$\lambda \space = \space \frac{6.626 \space \times \space 10^{-34} \space 2.998 \space \times \space 10^8}{1.09 \space \times \space 10^{-19}}$

$\lambda \space = \space \frac{ 1 9. 8 6 4 7 4 8\space \times \space 10^{-34} \space 10^8}{1.09 \space \times \space 10^{-19}}$

By simplifying, we get:

$\lambda \space = \space 1.82 \space \times \space 10^-6 m$

So the wavelength of light is $\space 1.82 \space \times \space 10^-6 m$.

The wavelength of light  absorbed which is related to the electron transition is $\space 1.82 \space \times \space 10^-6 m$. The electron must absorb light in order to transition to a higher level of energy.

## Example

Find the wavelength of light which is related to the electron transition when an electron jumps from lower energy state to higher energy state.

We have to find the wavelength of light which is related to the electron transition when it jumps from lower level of energy to a higher level of energy.

We know that energy change is:

$\Delta E \space = \space 1.09 \space \times 10^{-19} \times j$

Planck constant  $h$ is $6.626 \space \times 10^{-34} js$.

And the speed of light is $2.998 \space \times 10^8 \frac{m}{s}$.

Now calculating the wavelength of light:

$\lambda \space = \space \frac{hc}{\Delta E}$

By putting values, we get:

$\lambda \space = \space \frac{6.626 \space \times \space 10^{-34} \space 2.998 \space \times \space 10^8}{1.09 \space \times \space 10^{-19}}$

$\lambda \space = \space \frac{ 1 9. 8 6 4 7 4 8\space \times \space 10^{-34} \space 10^8}{1.09 \space \times \space 10^{-19}}$

By simplifying, we get:

$\lambda \space = \space 1.82 \space \times \space 10^-6 m$

So the wavelength of light is $\space 1.82 \space \times \space 10^-6 m$.

The wavelength of light absorbed which is related to the electron transition is $\space 1.82 \space \times \space 10^-6 m$. The electron must absorb light in order to transition to a higher level of energy.