Question

How much energy is required to get a hydrogen atom to excite to n = 5?

Answer 1

Answer:

$2.09\cdot 10^{-18} J$

Explanation:

The energy levels of a hydrogen atom are given by the formula

$E_n = -13.6 \frac{1}{n^2}$ [eV]

where n is the number of the level.

Therefore, the energy of the ground state is

$E_1 = -13.6 eV$

While the energy of the level n = 5 is

$E_5 = -13.6 \frac{1}{5^2}=-0.54 eV$

So, the energy that a hydrogen atom needs to excite from n = 1 to n = 5 is

$\Delta E = E_5 - E_1 = -0.54-(-13.6)=13.06 eV$

And converting into Joules,

$\Delta E = 13.06 \cdot (1.6\cdot 10^{-19})=2.09\cdot 10^{-18} J$