Question

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

Answer 1

`2.09\cdot 10^(-18) J`

Step-by-step explanation:

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

`E_n = -13.6 (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 (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`