physics help

Question

Earlier when you read about the energy levels of hydrogen, you were introduced to an energy level diagram. You preformed a n = 1 to n = ∞ transition and observe the energy state data.

According to the applet, what is the radius of the n = ∞ energy level? 

2- If an electron is initially in the ground state, how much energy, in eV's, must be absorbed by the atom for a transition to the n = ∞ energy level to occur?

Answer 1

(1)

When the value of n is higher, the number of principal electronic shells is greater. This causes a greater distance between the farthest electron and the nucleus. As a result, the size of the atom and its atomic radius increases.

So as the energy level reaches to infinty (n = ∞) , greater distance between the farthest electron and the nucleus .

Answer 2

(2)

The n = 1 state is known as the ground state, while higher n states are known as excited states.

If the electron in the atom makes a transition from a particular state to a lower state, it is losing energy.

To conserve energy, a photon with an energy equal to the energy difference between the states will be emitted by the atom.

In the hydrogen atom,  the energy of the emitted photon can be found using:

E = (13.6 eV) [1/n_f² - 1/n_i²]

Given n_f = ∞  and n_i = 1 .

E = (13.6 eV) [1/∞² - 1/1²]

E = (13.6 eV) [0 - 1]

E = - 13.6 eV .

The amount of energy to be absorbed is  - 13.6 eV .