Question

What is the calculated energy (in kJ) of light emitted in the hydrogen spectrum, when an electron falls from the 5th energy level to the 4th energy level?

Answer 1

Given that,

An electron falls from the 5th energy level to the 4th energy level.

To find,

The energy (in kJ) of light emitted in the hydrogen spectrum.

Solution,

When electron makes transition from one energy level to another, then energy is given by :

$\Delta E=-2.18\times 10^{-18}\ \text{J}(\dfrac{1}{n_f^2}-\dfrac{1}{n_i^2})$

We have, $n_f=4$ and $n_i=5$

So,

$\Delta E=-2.18\times 10^{-18}\ \text{J}(\dfrac{1}{4^2}-\dfrac{1}{5^2}})\\\\\Delta E=4.90\times 10^{-20}\ J$

or

$\Delta E=4.9\times 10^{-23}\ \text{kJ}$

So, the energy of the emitted light is $4.9\times 10^{-23}\ \text{kJ}$