Question

An experiment called the Stern-Gerlach experiment helped establish the existence of electron spin. In this experiment, a beam of silver atoms is passed through a magnetic field, which deflects half of the silver atoms in one direction and half in the opposite direction. The separation between the two beams increases as the strength of the magnetic field increases. (a) What is the electron configuration for a silver atom? (b) Would this experiment work for a beam of cadmium (Cd) atoms? (c) Would this experiment work for a beam of fluorine (F) atoms?

Short answer

a) The electron configuration for a silver atom is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 4d^{10} 5p^6\] b) Yes, this experiment would work for a beam of cadmium atoms because they have unpaired electron spins. c) No, this experiment would not work for a beam of fluorine atoms because they have paired electron spins.

Step-by-step solution

(Step 1: Determine the electron configuration of silver)

(To determine the electron configuration of silver, we first need to find the atomic number of silver (Ag). The atomic number of Ag is 47. The electron configuration can be found by distributing electrons in various energy levels and orbitals as per increasing energy and following the Pauli Exclusion principle.)

(Step 2: Electron configuration for a silver atom)

(Using the periodic table and Aufbau principle, we distribute electrons to form the electron configuration for Ag. The electron configuration for Ag is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^9 5p^6\] However, this configuration is not correct due to special stability achieved by completely filled or half-filled orbitals. So, one electron from the 5s orbital will move to the 4d orbital to make it fully filled. Therefore, the correct electron configuration for Ag is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 4d^{10} 5p^6\])

(Step 3: Discuss the Stern-Gerlach experiment for cadmium atoms)

(To analyze the possibility of the Stern-Gerlach experiment to work for cadmium (Cd) atoms, we need to determine the electron configuration of Cd. The atomic number of Cd is 48. The electron configuration for Cd is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 5d^1\] Both Ag and Cd have unpaired electron spins; therefore, the Stern-Gerlach experiment will work for a beam of cadmium atoms.)

(Step 4: Discuss the Stern-Gerlach experiment for fluorine atoms)

(To analyze the possibility of the Stern-Gerlach experiment working for fluorine (F) atoms, we need to determine the electron configuration of F. The atomic number of F is 9. The electron configuration for F is: \[1s^2 2s^2 2p^5\] The fluorine atom has paired electron spins; thus, the Stern-Gerlach experiment will not work for a beam of fluorine atoms.) Summary: a) The electron configuration for a silver atom is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 4d^{10} 5p^6\] b) The Stern-Gerlach experiment will work for a beam of cadmium atoms due to their unpaired electron spins. c) The Stern-Gerlach experiment will not work for a beam of fluorine atoms due to their paired electron spins.