(a) The characteristic emission from Ca occurs at 422.7 nm and corresponds to an electron going from a 4p orbital to a 4s orbital. Calculate the energy of the electron in the 4p orbital. Calculate Zeff for the electron in the 4p orbital.
(b) The same 4p to 4s transition in potassium occurs at 769 nm. Calculate the energy of an electron in the 4p orbital of potassium and Zeff for this electron.
(c) Explain the differences between your answer to parts (a) and (b).
To calculate the energy of an electron in a given orbital, we can use the equation:
E = -13.6 * (Zeff)^2 / n^2
Where E is the energy, Zeff is the effective nuclear charge, and n is the principal quantum number.
(a) For calcium (Ca), we are given that the electron transition occurs from a 4p orbital to a 4s orbital. Let's first calculate the energy of the electron in the 4p orbital.
Using the above equation, we substitute Zeff = 20 (since calcium has atomic number 20) and n = 4 (for the 4th energy level corresponding to the 4p orbital):
E = -13.6 * (20)^2 / 4^2
E = -13.6 * 400 / 16
E = -13.6 * 25
E = -340 eV
So, the energy of the electron in the 4p orbital of calcium is -340 electron volts (eV).
To calculate Zeff for the electron in the 4p orbital, we need to consider the shielding effect of other electrons. Since the electron in the 4p orbital is experiencing shielding from the 4s and 3d electrons, Zeff is less than the actual atomic number.
(b) For potassium (K), we are given the same 4p to 4s transition, but at a different wavelength.
Let's calculate the energy of the electron in the 4p orbital of potassium.
Using the same equation as before, we substitute Zeff = 19 (since potassium has atomic number 19) and n = 4:
E = -13.6 * (19)^2 / 4^2
E = -13.6 * 361 / 16
E = -13.6 * 22.5625
E = -306.85 eV
So, the energy of the electron in the 4p orbital of potassium is -306.85 eV.
To calculate Zeff for the electron in the 4p orbital, we consider the shielding effect of other electrons, including those in lower energy levels (4s and 3d). The difference in Zeff for potassium compared to calcium arises due to the different electron configurations and shielding effects of the particular atoms.
(c) The differences in the energy and Zeff values between calcium and potassium arise due to their different atomic structures and electron configurations. Both elements have different numbers of protons and different electron arrangements, leading to different levels of electron shielding and Zeff values.
Additionally, the energy of the electron in the 4p orbital is different because the energy levels in different elements are not the same. The energy levels are determined by the atomic structure and the specific electron configuration of each element.