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**.

## Expert Answer

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 $.

## Numerical Answer

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 **s****implifying**, 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**.