An electron accelerates through a 12.5 V potential difference, starting from rest, and then collides with a hydrogen atom, exciting the atom to the highest energy level allowed. List all the possible quantum-jump transitions by which the excited atom could emit a photon. 4 rightarrow 3 4 rightarrow 2 4 rightarrow 1 3 rightarrow 2 3 rightarrow 1 2 rightarrow 1

Initial state    Final state

     3           ⇒        2

     3           ⇒        1

     2          ⇒         1

Explanation:

For this exercise we must use Bohr's atomic model

         E = - 13.606 / n²

where is the value of 13.606 eV is the energy of the ground state and n is the integer.

The energy acquired by the electron in units of electron volt (eV)

          E = e V

          E = 12.5 eV

all this energy is used to transfer an electron from the ground state to an excited state

        ΔE = 13.6060 (1 / n₀² - 1 / n²)

the ground state has n₀ = 1

       ΔE = 13.606 (1 -  1/n²)

        1 /n² = 1 - ΔE/13,606

         1 / n² = 1 - 12.5 / 13.606

         1 / n² = 0.08129

          n = √(1 / 0.08129)

          n = 3.5

 since n is an integer, maximun is

         n = 3

because it cannot give more energy than the electron has

From this level there can be transition to reach the base state.

Initial state    Final state

     3           ⇒        2

     3           ⇒        1

     2          ⇒         1

moving ball hits still ball. mover stops, hit ball moves. momentum transfer.

grav force prop 1/r squared 2r all squared is 4rsquared 1/4rsquared quartered