Question

2. Define fermion and boson AND give examples of each. 3. To what orbitals may electrons in a 4d orbital make spectroscopic transitions in a hydrogen atom? 4. Calculate wavelength of the n=6 transition in the Paschen series for a hydrogen atom 5. What terms and levels arise from the ground-state configuration of carbon? Which term has the lowest energy? 6. List and simplify the complete wavefunction for a 2s orbital.

Answer 1

Answer 2: The fermion is defined as follows:

A fermion is defined as a particle that obeys the Pauli exclusion principle and follows Fermi Dirac statistics i.e. It describe a distribution of particles over energy states in systems consisting of many identical particles that obey the "Pauli exclusion principle". A fermion can be an elementary particle, such as the electron, or it can be a composite particle, such as the proton. It has half odd integer spin such as 1/2, 3/2.

The boson can be defined as follows:

A boson is defined as a particle that follows Bose -Einstein statistics i.e. It describe one of two possible ways in which a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic equilibrium. Examples of bosons are fundamental particles such as photons, gluons, and W and Z bosons. Some composite particles are also bosons, such as mesons etc. An important characteristic of bosons is that there is no restriction on the number of them that occupy the same quantum state. Bose–Einstein statistics encourages identical bosons to crowd into one quantum state.

Answer 3: To determine to what orbitals may electrons in a 4d orbital make spectroscopic transitions in a hydrogen atom we have to apply a rule known as selection rule. In our case l =2 so the final orbital should have f = 1 or 3 (as per selection rule). Thus an electron may make transition to any np orbital depending upon the value of m or any nf orbital.

Answer 4: The wavelength of n =6 transition in the Paschen series for a hydrogen atom is calculated as follows:

From the given formula we can calculate the wavelength of transition in the Paschen series i.e.

1/$\lambda$ = RH X (1/nf2 -1/n2) where n = 4, 5, 6

R H (Rydberg constant for hydrogen) = 1.09677576 x 107 m

nf valuefor Paschen series is 3

Now putting values in the above equation we get as follows:

1/$\lambda$ =  1.09677576 x 107 m X (1/32 -1/62) = 1.09677576 x 107 m X (1/9 -1/36) = 1.09677576 x 107 m X (0.11 -0.02) = 1.09677576 x 107 m X (0.0822) =0.090 x 107 m or = 90.15 x 104 m

1/$\lambda$ = 90.15 x 104 m so solving for $\lambda$ we have = 1/90.15 x 104 m = 0.1109 x10-4 m = 1109 nm.

Answer 5: The terms and level which arise from the ground state configuration of carbon is as follows:

The electronic configuration is 1s22s22p2

We have two closed subshell. 1s and 2s which both give 1S0

we may concentrate on the p shell with two equivalent p electrons. In this we include only states thgat is allowed,

The term S subshell has lowest energy.

np np
ML	2 1 0 -1 -2	MS
1	0	-1
	(1+ 1-)
(1+ 0+)	(1+ 0-) (1- 0+)	(1- 0-)
(1+ -1+)	(1+ -1-) (0+ 0-) (-1+ 1-)	(1- -1-)
(-1+ 0+)	(-1+ 0-) (-1- 0+)	(-1- 0-)
	(-1+ -1-)