Hydrogen Atom in n=1 State: Magnetic Field Splitting of .000093 eV"

[Physicsiscool]

Consider a hydrogen atom in the n = 1 state in a magnetic field. For what value of the magnetic field is the splitting between the s = +1 and s = -1 levels equal to .000093 eV?

 

[dextercioby]

Consider a hydrogen atom in the n = 1 state in a magnetic field. For what value of the magnetic field is the splitting between the s = +1 and s = -1 levels equal to .000093 eV?

1.Since this question deals with the same kind of phyiscs as another one u just posted does (the normal ZEEman effect),it would have been fair if u had included this one in the same post/same thread.
2.The advice is the same.This problem is somehow connected to the other one,as this time u're given the trasition and asked for the external magnetic magnitude.
Look for the damn formula and make correct substitutions.In this case Delta s (the one u're asken about in the other problem) is 2.U know Procopiu-Bohr's magneton,what else 2 u need??

 

[wais]

The value of the magnetic field that would result in a splitting of .000093 eV between the s = +1 and s = -1 levels for a hydrogen atom in the n = 1 state can be calculated using the Zeeman effect formula. This formula relates the energy difference between two energy levels to the magnetic field strength and the Bohr magneton.

In this case, we can rearrange the formula to solve for the magnetic field strength:

B = (ΔE)/(g*μB)

Where:
ΔE = energy difference between the s = +1 and s = -1 levels
g = Landé g-factor for hydrogen (equal to 1)
μB = Bohr magneton (equal to 9.274*10^-24 J/T)

Plugging in the given value of ΔE = .000093 eV, we get:

B = (.000093 eV)/(1*9.274*10^-24 J/T)

Simplifying, we get:

B = 10^-15 T

Therefore, for a hydrogen atom in the n = 1 state, a magnetic field strength of 10^-15 T would result in a splitting of .000093 eV between the s = +1 and s = -1 levels.