What is the seperation energy ineV for Be3+ in the first excited state in eV?
To find the separation energy of Be3+ in the first excited state, we need to know the ionization energy of Be3+ in its ground state and the energy of the first excited state.
First, let's find the ionization energy of Be3+ in its ground state. The ionization energy is the energy required to remove an electron from an atom or ion. The atomic number of beryllium is 4, which means that neutral beryllium has 4 electrons. Be3+ has a charge of +3, which means it has lost 3 electrons and is left with only 1 electron.
The ionization energy can be found using the equation:
Ionization Energy (eV) = (Z^2 * 13.6) / n^2
Where Z is the effective nuclear charge (equal to the atomic number subtracted by the charge of the ion) and n is the principal quantum number of the electron being removed. In this case, Z = 4 - 3 = 1, and n = 1 (since we are finding the ionization energy of the ground state).
Plugging the values into the equation:
Ionization Energy = (1^2 * 13.6) / 1^2
Ionization Energy = 1 * 13.6
Ionization Energy = 13.6 eV
Now, let's find the energy of the first excited state of Be3+. The energy of an electron in a hydrogen-like ion can be found using the equation:
Energy (eV) = -13.6 / n^2
Where n is the principal quantum number of the electron's energy level. In this case, since we want the energy of the first excited state, n = 2.
Plugging the value into the equation:
Energy = -13.6 / 2^2
Energy = -13.6 / 4
Energy = -3.4 eV
Finally, to find the separation energy in eV, we subtract the energy of the first excited state from the ionization energy:
Separation Energy = Ionization Energy - Energy
Separation Energy = 13.6 eV - (-3.4 eV)
Separation Energy = 17 eV
Therefore, the separation energy of Be3+ in the first excited state is 17 eV.
1/wavelength = RZ^2(1/1^2 - 1/infinity)
R is Rydberg constant. You can look that up in (in meters)
The term of 1/infinity will be zero.
This will give you wavelength and you can convert to energy with E = hc/wavelength.
Z is the atomic number of Be