Consider the ground state of hydrogen. (a) Write down the possible values of the

Question

Consider the ground state of hydrogen. (a) Write down the possible values of the 4 quantum numbers (n, l, ml, ms) corresponding to this state. Note that if there is no external magnetic field (e.g. B = 0) then there are two degenerate levels corresponding to ms = 1/2 and ms = 1/2. (b) Assume that a magnetic field of 10 T is turned on. The two degenerate levels will then be split into levels with different energies. Calculate the magnitude E of the shift (in eV) of each of the two levels from the original ground state energy along with the resulting spacing E = 2E between the two levels.

Explanation / Answer

We know that

The electronic configuration of hydrogen is1S1

The ground state of hydrogen atomic number is 1

Therefore n=1,l=0 and S =(1/2) ,ml =0,ms =(-1/2) and (1/2)

b)

The energy shift is given by

E =g*ehB/4pimc2

where g is the lande ga factor g =1+J(J+1)-l(l+1)-s(s+1)/2J(J+1)

Here g =1

So ,E =(1)*6.625*10-34*1.6*10-19*10/4*3.14*9.1*10-31*(3*108)2 =9.274*10-23J

We know that 1eV =1.6*10-19J then E =5.789*10-4eV

Therefore the total shift =2E =2*5.789*10-4eV =1.157*10-3eV

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